Practice Questions for Business Statistics

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Chapter: Regression Analysis

Contents:

1148-2 "In order to have a correlation coefficient between traits A and B,"

1426-3 Suppose a 95% confidence interval for the slope (BETA)

1526-1 0.80 is an estimate of ___________.

1543-1 Calculation of confidence interval for b(2) consists of

1656-2 you test the hypothesis that the slope (BETA) is zero

1726-1 YHAT = -2.5X + 60. We compute the average price per widget if 30

1731-1 "Which, if any, of these amounts do you recommend that the king use"

1732-1 "An economist is interested in the possible influence of ""Miracle Wheat"""

1733-1 why do we need to be concerned with the range of the independent (X)

1738-1 Extrapolation

1739-1 Interpolation

1751-1 What is Y(2)?

1753-1 Make a scatterplot for the following data.

1755-1 r**2 = (.93**2) = 0.871. What does it mean in this case?

1757-1 The regression line is YHAT(i) = -8.26 + 1.17(X(i)). Plot it

1762-2 A scatter diagram is a graphic device for detecting and analyzing

1763-1 Scatter Diagram

1861-3 A researcher finds that the correlation between the personality

1991-1 What model for Y is suggested by each of the following graphs?

1993-1 Propose a model (including a very brief indication of symbols used

1994-1 Propose a model that might be used to predict % alcohol in blood

2088-1 What is your estimate of the average height of all trees having

2091-1 Is this evidence consistent with the claim that the number of fleas is

2123-1 Describe the relation between income and experience

2135-1 T TEST OF A REGRESSION COEFFICIENT

2138-2 What is the smallest significance level at which you would reject

2443-1 The coefficient of multiple determination is:

2443-2 An interpretation of r = 0.5 is that the following part of

2444-2 Which of the following values of r indicates the most accurate

2445-1 If the correlation between age of an auto and money spent for repairs

2445-2 "If the coefficient of correlation equals 0.61, it indicates that the"

2446-2 test had a correlation of .40. What percentage of the variance do

2449-1 "If in a given experiment r = 0.70, then 49 percent of the variation of"

2449-2 The coefficient of determination can have values between

2449-3 the proportion of the variation in Y which is explained by Y's linear

2469-1 is -0.95. Which of the following conclusions is correct?

2470-1 plotted on a diagram (given below). A statistician asserts that the

2471-2 A sample correlation coefficient of -1 (minus one) tells us that

2471-3 The appropriate statistical analysis is:

2472-1 correlation of 0.75 was found. This indicates that the relationship

2473-1 The figure below indicates that Variable A and Variable B are:

2474-1 The correlation between Variable A and Variable B in the figure below

2475-1 -0.73. Which of the following may be concluded?

2475-2 If we obtain a negative r

2476-1 was found to be -1.08. On the basis of this you would

2481-1 the coefficient of correlation is.10. What does this mean?

2481-3 indicate a situation where more than half of the variation

2482-1 what is the approximate value of the correlation coefficient?

2484-1 The correlation coefficient for X and Y is known to be zero.

2486-1 [12 inches = one foot; 16 ounces = one pound]

2487-2 coefficient of correlation of -.90 was obtained. This indicates

2487-4 no comparison can be made between r=-.80 and r=+.80

2488-3 What would you guess the value of the correlation coefficient to be for

2490-4 between height measured in feet and weight measured in pounds is +.68.

2491-2 The sign (plus or minus) of a correlation coefficient indicates

2491-3 a neuroticism test and scores on an anxiety test is high and positive

2492-2 "In correlational analysis, when the points scatter widely about the"

2494-1 "Explain what correlation coefficients of -1, 0 and 1 mean, using"

2503-2 what conclusions might be drawn?

2504-1 to determine wrestling ability. EXPLAIN THIS STATEMENT.

2505-1 Write an interpretation of each of the following correlations:

2513-1 Discuss briefly the distinction between correlation and causality.

2514-4 "If r is close to + or -1, we shall say there is a strong correlation,"

2515-1 then geometrically speaking the regression of Y on X yields

2515-3 is proof of a cause-effect relationship between the variables.

2516-1 association rather than causation

2516-2 r is only an estimate of the true correlation coefficient

2518-3 Correlation Coefficient

2519-1 Simple Correlation or Simple Regression

2524-1 Complete the following Analysis of Variance Table

2532-1 Tukey's HSD (at ALPHA = .05) = 5.57113

2545-1 Individual statistical comparisons between pairs of means

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Questions:

1148-2

    Q:  In order to have a correlation coefficient between traits A and B,
        it is necessary to have:

        a.  one group of subjects, some of whom possess characteristics of
            trait A, the remainder possessing those of trait B

        b.  measures of trait A on one group of subjects and of trait B on
            another group

        c.  two groups of subjects, one which could be classified as A or
            not A, the other as B or not B

        d.  measures of traits A and B on each subject in one group

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1426-3

    Q:  True or False?  If False, correct it.

        Suppose a 95% confidence interval for the slope (BETA) of the straight
        line regression of Y on X is given by -3.5 < BETA < -0.5.  Then a two-
        sided test of the hypothesis H(0): BETA = -1 would result in rejection
        of H(0) at the 1% level of significance.

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1526-1

    Q:  An investigator has used a multiple regression program on 20 data points
        to obtain a regression equation with 3 variables. Part of the computer
        output is:

             Variable     Coefficient       Standard Error of b(i)

                 1             0.45                 0.21
                 2             0.80                 0.10
                 3             3.10                 0.86

             a.  0.80 is an estimate of ___________.

             b.  0.10 is an estimate of ___________.

             c.  Assuming the responses satisfy the normality assumption, we
                 can be 95% confident that the value of BETA(2) is in the interval,
                 _______ +/- [t(.025) * _______], where t(.025) is the criti-
                 cal value of the student's t distribution with ____ degrees
                 of freedom.

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1543-1

    Q:  A computer program for multiple regression has been used to fit
        YHAT(j) = b(0) + b(1)*X(1j) + b(2)*X(2j) + b(3)*X(3j)

        Part of the computer output includes:

        i       b(i)    S(b(i))
        0        8        1.6
        1        2.2       .24
        2        -.72      .32
        3         .005     .002

        a.  Calculation of confidence interval for b(2) consists of _______
            +/- (a student's t value) (_______)
        b.  The confidence level for this interval is reflected in the value
            used for _______.
        c.  The degrees of freedom available for estimating the variance are
            directly concerned with the value used for _______.

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1656-2

    Q:  True or False?  If False, correct it.

        Suppose you are performing a simple linear regression of Y on X and
        you test the hypothesis that the slope (BETA) is zero against a two-
        sided alternative.  You have n = 25 observations and your computed
        test (t) statistic is 2.6.  Then your P-value is given by .01 < P <
        .02, which gives borderline significance (i.e. you would reject H(0)
        at ALPHA = .02 but fail to reject H(0) at ALPHA = .01).

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1726-1

    Q:  We are interested in finding the linear relation between the number
        of widgets purchased at one time and the cost per widget.  The
        following data has been obtained:

        X:  Number of widgets purchased-- 1   3   6  10   15
        Y:  Cost per widget(in dollars)--55  52  46  32   25

        Suppose the regression line is YHAT = -2.5X + 60.  We compute the
        average price per widget if 30 are purchased and observe:

        a.  YHAT = -15 dollars; obviously, we are mistaken; the prediction
            YHAT is actually +15 dollars.
        b.  YHAT = 15 dollars, which seems reasonable judging by the data.
        c.  YHAT = -15 dollars, which is obvious nonsense.  The regression
            line must be incorrect.
        d.  YHAT = -15 dollars, which is obvious nonsense.  This reminds us
            that predicting Y outside the range of X values in our data is a
            very poor practice.

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1731-1

    Q:  Once upon a time there was a wizard who invented a means of amplifying
        the sounds produced by the king's musicians.  By dropping a gold coin
        into a slot, the king could amplify sound:  1 coin - 1 fold
                                                    2 coins - 2 fold
                                                    etc.

        The wizard persuaded the king to write down a number indicating the
        pleasure he experienced from various performances of the musicians.
        Later he presented these results:

                        Coins           Pleasure
                          0                10
                          1                15
                          2                20
                          3                25

        Said the wizard, "Clearly, your majesty, we have found the fountain of
        pure joy.  The more coins, the greater amplification, and the greater
        your pleasure."

        Which, if any, of these amounts do you recommend that the king use for
        his next investment in amplification (you should suggest more than one
        if appropriate).
        Explain your advice.

        a.  3 coins
        b.  100 coins
        c.  1000 coins
        d.  4 coins
        e.  10 coins

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1732-1

    Q:  An economist is interested in the possible influence of "Miracle Wheat"
        on the average yield of wheat in a district.  To do so he fits a linear
        regression of average yield per year against year after introduction of
        "Miracle Wheat" for a ten year period.  The fitted trend line is

                YHAT(j) = 80 + 1.5*X(j)
                        (Y(j): Average yield in j year after introduction)
                        (X(j): j year after introduction).

        a.  What is the estimated average yield for the fourth year after
            introduction?
        b.  Do you want to use this trend line to estimate yield for, say, 20
            years after introduction?  Why?  What would your estimate be?

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1733-1

    Q:  In a linear regression, why do we need to be concerned with the range
        of the independent (X) variable?  (Be brief, coherent, and legible.)

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1738-1

    Q:  Define the following term and give an example of its use.
        Your example should not be one given in class or in a handout.

        Extrapolation

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1739-1

    Q:  Define the following term and give an example of its use.
        Your example should not be one given in class or in a handout.

        Interpolation

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1751-1

    Q:  A data set consists of:

                Case          X          Y
                 1            7         101
                 2            9         119
                 3            1         121
                 4            5         108
                 5            2         112

        a.  What is Y(2)?
        b.  What is X(2)?
        c.  What is SUM(i=1,5) (X(i))?
        d.  What is SUM(i=1,5) (X(i)**2)?
        e.  Suppose that the relation between Y and X is said to be
            Y(j) = 15 + 10*X.
                1.  What is YHAT(4)?
                2.  What is e(4)?
                3.  What is SUM(j=1,5) (e(j)**2) for this relation?
        f.  Plot Y vs X.

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1753-1

    Q:  Make a scatterplot for the following data. 

        X  |  Y
        -------
        1  |  2
        4  |  8
        0  | -1
        3  |  6
        Regression equation is:  YHAT(i) = -.65 + 2.2X(i)

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1755-1

    Q:  Consider the following paired data:

             X  |  3   2   -1   -4
          ------------------------------
             Y  | -4  -1    2    3

             a.  Make a scatterplot for this data.
             b.  r**2 = (.93**2) = 0.871. What does it mean in this case?

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1757-1

    Q:  Consider the set of data below.  Make a scatterplot. The
    regression line is YHAT(i) = -8.26 + 1.17(X(i)). Plot it 
    (approximately) on your scatterplot.

        X |   8  10  11  12
        -------------------
        Y |   2   2   4   7

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1762-2

    Q:  True or False?  If False, correct it.

        A scatter diagram is a graphic device for detecting and analyzing
        association between two variables.

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1763-1

    Q:  Define the following term and give an example of its use.
        Your example should not be one given in class or in a handout.

        Scatter Diagram

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1861-3

    Q:  A researcher finds  that  the  correlation  between  the  personality
        traits "greed" and "superciliousness" is -.40.  What percentage of the
        variation in greed can be explained by the relationship with
        superciliousness?

        a)  60%
        b)   0%
        c)  16%
        d)  20%
        e)  40%

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1991-1

    Q:  What model for Y is suggested by each of the following graphs?

        a.  Y                               b.  Y
            |                                   |
            |                                   |
            |                                   *
            |                                   |
            |                     *             |
            |                                   |
            |                                   |
            *                                   |
            |                                   |
            ----------------------------> X     ---------------*------------> X

        c.  |                               d.  |
            |                                   |                         *
            |                                   |                       *
            |                                   |                *    *
            |                                   |                   *
            |                                   |           *
            |  *                      *         |
            |                                   |       *
            |                                   |
            |                                   |   *
            |                                   |
            ----------------------------> X     ----------------------------> X

        e.  Y
            |
            |                                    NOTE:  In order to complete the
            |                                           above graphs,  for a.-c.
            |                *                          connect  the  *'s  with
            |          *            *                   straight lines  and for
            |                          *                d.-e. connect  the  *'s
            |     *                                     with smooth curves.
            |
            *
            |
            ----------------------------> X

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1993-1

    Q:  Suppose that you have at your disposal the information below for each
        of 30 drivers.  Propose a model (including a very brief indication of
        symbols used to represent independent variables) to explain how miles
        per gallon vary from driver to driver on the basis of the factors
        measured.

        Information:
                1.  miles driven per day
                2.  weight of car
                3.  number of cylinders in car
                4.  average speed
                5.  miles per gallon
                6.  number of passengers

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1994-1

    Q:  Suppose that you have been appointed Grand Nabob of Temperance.  In
        becoming a master of your new assignment you obtain the data listed
        below on 20 seniors at UNH.

                1.  percent alcohol in blood
                2.  number of drinks consumed
                3.  weight
                4.  sex (male or female)
                5.  time spent in consuming drinks.

        Propose a model that might be used to predict % alcohol in blood on the
        basis of number of drinks, etc.  (be sure to define symbols used for
        independent variables).

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2088-1

    Q:  Suppose one collected the following information where X is diameter
        of tree trunk and Y is tree height.

            X    Y
            -    -
            4    8
            2    4
            8   18
            6   22
           10   30
            6    8

           Regression equation:
                YHAT(i) = -3.6 + 3.1*X(i)
            What is your estimate of the average height of all trees having a
            trunk diameter of 7 inches?

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2091-1

    Q:  The manufacturers of a chemical used in flea collars claim that under
        standard test conditions each additional unit of the chemical will
        bring about a reduction of 5 fleas (i.e. where X(j) = amount of chemical
        and Y(J) = B(0) + B(1)*X(J) + E(J), H(O):  B(1) = -5)

        Suppose that a test has been conducted and results from a computer
        include:  Intercept = 60
                  Slope = -4
                  Standard error of the regression coefficient = 1.0

        Degrees of Freedom for Error = 2000
        95% Confidence Interval for the slope -2.04, -5.96

        Is this evidence consistent with the claim that the number of fleas is
        reduced at a rate of 5 fleas per unit chemical?

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2123-1

    Q:  Suppose that a report contains this graph:

                          |
                          |
            Annual Income |
            (thousands of |
             $ per year)  |
                          |
                       50 +                             *
                          |                   *
                          |
                          |
                          |
                          |
                          |
                          |
                          |         *
                          |
                       25 +
                          |
                          |
                          |
                          |
                          *
                          |
                          |
                          |
                          |
                          ----------+---------+---------+---------->
                                   10        20        30
                                Years of Experience in Trade

                           (Note:  to complete graph, connect the *'s
                                   with a smooth curve.)

        a.  What does the graph indicate as annual income for someone with no
            experience in the trade?

        b.  Describe the relation between income and experience over the inter-
            val from 0 to 20.

        c.  Describe the relation between income and experience over the inter-
            val 20 to 30.

        d.  Describe the overall graph.

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2135-1

    Q:  Define the following term and give an example of its use.
        Your example should not be one given in class or in a handout.

        T TEST OF A REGRESSION COEFFICIENT

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2138-2

    Q:  When testing the estimate of a linear regression coefficient based on a
        sample of 14 (X,Y) pairs, the calculated value  of the F-statistic  was
        6.92   What is the smallest significance level at which you would  re-
        ject the hypothesis H(O):  BETA = 0 against H(A):  BETA =/= 0?

        a.  .01             d.  .05
        b.  .02             e.  .1
        c.  .025

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2443-1

    Q:           Y            X(1)          X(2)
                --------------------------------
                -2             1            -2
                -1             2             0
                 6             3             0
                 9             6             2

        The coefficient of multiple determination, calculated as:

             R**2 = (explained variation using X(1) and X(2) in the
                    regression)/(total variation)

        is:

        a.  142/122
        b.  74/86
        c.  a negative number
        d.  185/122
        e.  None of the above
ANOVA
          df     SS    MS    F
Regression  2     74    37    3.08333333
Residual    1     12    12
Total       3     86

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2443-2

    Q:  An interpretation of r = 0.5 is that the following part of
        the Y-variation is associated with variation in X:

             a.  most               d.  one quarter
             b.  half               e.  none of these.
             c.  very little

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2444-2

    Q:  Which of the following values of r indicates the most accurate
        prediction of one variable from another?

        a)  r = 1.18          b)  r = -.77        c)  r = .68

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2445-1

    Q:  If the correlation between age of an auto and money spent for repairs
        is +.90

           a.  81% of the variation in the money spent for repairs is
               explained by the age of the auto
           b.  81% of money spent for repairs is unexplained by the age of
               the auto
           c.  90% of the money spent for repairs is explained by the age of
               the auto
           d.  none of the above

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2445-2

    Q:  If the coefficient of correlation equals 0.61, it indicates that the
        proportion of the variation in the dependent variable explained by the
        variation in the independent variable is

           a.  37%       b.  61%       c.  98%       d.  cannot be determined

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2446-2

    Q:  Suppose that college grade-point average and verbal portion of an IQ
        test had a correlation of .40.  What percentage of the variance do
        these two have in common?
        a.  20        b.  16        c.  40        d.  80

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2449-1

    Q:  True or False?

        If in a given experiment r = 0.70, then 49 percent of the variation of
        the Y's can be accounted for (is perhaps caused) by differences in the
        variable X.

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2449-2

    Q:  True or false?  If false, explain why.

        The coefficient of determination can have values between
        -1 and +1.

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2449-3

    Q:  True or False?  If False, correct it.

        With respect to regression,  the sample correlation coefficient r is
        the proportion of the variation in Y which is explained by Y's linear
        dependence on X.

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2469-1

    Q:  We are interested in finding the linear relation between the number
        of widgets purchased at one time and the cost per widget.  The
        following data has been obtained:

        X:  Number of widgets purchased-- 1   3   6  10   15
                     (in hundreds)
        Y:  Cost per widget(in dollars)--55  52  46  32   25

        Suppose the correlation between X and Y is -0.95.  Which of the
        following conclusions is correct?

        a.  The linear relation between X and Y is weak, and Y decreases
            when X increases.
        b.  The linear relation between X and Y is strong, and Y decreases
            when X increases.
        c.  The linear relation between X and Y is strong, and Y increases
            when X increases.
        d.  The linear relation between X and Y is weak, and Y increases
            when X increases.

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2470-1

    Q:  Suppose pairs of data values (X(i),Y(i)) have been gathered  and  are
        plotted on a diagram (given below).  A statistician asserts that the
        product-moment correlation between X and Y in this case is very low.
        Which of the following comments makes the most sense?

        Y|       .
         |      . .                 .
         |     .  .                . .
         |       .                 .. .
         |       ..              . .    ..
         |        .              ..     .  .
         |        .   .          .        .
         |         ..           .          . .
         |          . .       .  .           .
         |            .        ..            .
         |              ..    .              ..
         |                 . .               .  .
         |                ..
         |
         |
         |
         |
         |
         |__________________________________________
                                                   X

        a.  The statistician is wrong,  because knowing X lets us predict the
            average value of Y quite accurately.
        b.  The statistician is wrong,  because X and Y increase and decrease
            together.
        c.  The statistician is right,  because the correlation measures  how
            much linear relationship there is,  and  the relationship is cer-
            tainly not linear.

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2471-2

    Q:  Consider a sample least squares regression analysis between a dependent
        variable (Y) and an independent variable (X).  A sample correlation
        coefficient of -1 (minus one) tells us that

        a.  there is no relationship between Y and X in the sample
        b.  there is no relationship between Y and X in the population
        c.  there is a perfect negative relationship between Y and X in the
            population
        d.  there is a perfect negative relationship between Y and X in the
            sample.

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2471-3

    Q:  In a study of the relationship between intelligence and  achievement,
        scores  on  the  Dorge-Thorndike  Intelligence  Test and the Stanford
        Achievement Test are collected from a large group of students.  The
        appropriate statistical analysis is:

        a)  the correlation coefficient
        b)  the analysis of variance.
        c)  the t-test

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2472-1

    Q:  In a study of the relationship between self-concept and achievement, a
        correlation of 0.75 was found.  This indicates that the relationship
        between these two variables is:

        a)  weak and positive
        b)  strong and positive
        c)  weak and negative
        d)  strong and negative
        e)  one of independence

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2473-1

    Q:  The figure below indicates that Variable A and Variable B are:

                  |
         High  |        *
                  |   *  A
                  |          *  *
                  |    *           *
                  |       *    *      *
                  |
                  |       *         *
        Variable  |         *
               B  |            *       *
                  |        *  *
                  |          *    *       *
                  |          *   *
                  |                 *
                  |                        *
             Low  |                   *   B
                  -------------------------------------------->
                    Low                                  High
                                   Variable A

        NOTE:  Connect letters A and B with a straight line segment to complete
               the figure.

        a.  positively related
        b.  negatively related
        c.  independent

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2474-1

    Q:  The correlation between Variable A and Variable B in the figure below
        indicates that:

                  |
            High  |       *
                  |  *  A
                  |          *  *
                  |    *          *
                  |      *
                  |            *   *
                  |     *         *
        Variable  |         *     * *
               B  |       *   *
                  |     *   *   *       *
                  |           *    *     * *
                  |          *   *        *    *
                  |                          *
                  |           *    *
                  |                    *         *
             Low  |                  *    *   B   *
                  ---------------------------------------->
                   Low                                High
                                 Variable A

        NOTE:  Connect letters A and B with a straight line segment to complete
               the figure.

        a.  increases in Variable A cause decreases in Variable B.
        b.  increases in Variable A are accompanied by decreases in Variable B.
        c.  increases in one variable are unrelated to increases in the other.

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2475-1

    Q:  The correlation between anxiety and performance on complex tasks is
        -0.73.  Which of the following may be concluded?

        a.  as anxiety increases, performance on complex tasks improves;
        b.  as performance on complex tasks improves, anxiety tends to decrease;
        c.  high levels of anxiety cause poor performance on complex tasks;
        d.  as anxiety decreases, so does performance.

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2475-2

    Q:  If we obtain a negative r (Pearson r:  a coefficient of correlation)
        this means that:     (let's say r is -.75)

        a.  individuals scoring high on one variable tend to score low
            on the other variable.

        b.  individuals scoring high on one variable tend to score high
            on the other variable.

        c.  there is no relationship between the two variables.

        d.  the relationship is in the opposite direction to the one pre-
            dicted.

        e.  we have made an error.

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2476-1

    Q:  A correlation between college entrance exam grades and scholastic
        achievement was found to be -1.08.  On the basis of this you would
        tell the university that:

        a.  the entrance exam is a good predictor of success.
        b.  they should hire a new statistician.
        c.  the exam is a poor predictor of success.
        d.  students who do best on this exam will make the
            worst students.
        e.  students at this school are underachieving.

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2481-1

    Q:  Under a "scatter diagram" there is a notation that the coefficient of
        correlation is .10.  What does this mean?
            a.  plus and minus 10% from the means includes about 68% of the
                cases
            b.  one-tenth of the variance of one variable is shared with the
                other variable
            c.  one-tenth of one variable is caused by the other variable
            d.  on a scale from -1 to +1, the degree of linear relationship
                between the two variables is +.10

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2481-3

    Q:  Which, if any, of the values listed below for a correlation coefficient
        indicate a situation where more than half of the variation in one
        variable is associated with variation in the other variable?

        a.  r = -.7
        b.  r = .3
        c.  r = -.9
        d.  r = .6
        e.  r = 1.0

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2482-1

    Q:                  ]                       X
                     25-]
                        ]
                     20-]                X
                        ]                            X
        Tail         15-]           X
        Length          ]         X
                     10-]              X
                        ]
                      5-X                 X
                        ]
                        ]____X______________________
                         0          5         10

                           Horn Length

        On the basis of the above plot of horn length versus tail length of
        peppermint flavored unicorns, what is the approximate value of the
        correlation coefficient?

        a.  -1
        b.  -.6
        c.  0
        d.  +.6
        e.  +1

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2484-1

    Q:  The correlation coefficient for X and Y is known to be zero.  We then
        can conclude that:

        a.  X and Y have standard distributions
        b.  the variances of X and Y are equal
        c.  there exists no relationship between X and Y
        d.  there exists no linear relationship between X and Y
        e.  none of these

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2486-1

    Q:  Suppose the Pearson correlation coefficient between height as measured
        in feet versus weight as measured in pounds is 0.40.  What is the cor-
        relation coefficient of height measured in inches versus weight measured
        in ounces?  [12 inches = one foot;  16 ounces = one pound]

        a.  .4                   d.  cannot be determined from information given
        b.  .3                   e.  none of these
        c.  .533

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2487-2

    Q:  In a study to determine the relationship between two variables, a
        coefficient of correlation of -.90 was obtained.  This indicates

           a.  The computations are wrong since r cannot be negative
           b.  There is a fairly low relationship between the two
               variables
           c.  The coefficient of determination is the square root of .90
           d.  Variable Y tends to decrease as Variable X increases

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2487-4

    Q:  A coefficient of correlation of -.80

           a.  is lower than r=+.80
           b.  is the same degree of relationship as r=+.80
           c.  is higher than r=+.80
           d.  no comparison can be made between r=-.80 and r=+.80

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2488-3

    Q:  What would you guess the value of the correlation coefficient to be for
        the pair  of variables:   "number of man-hours worked" and  "number  of
        units of work completed"?

        a)  Approximately 0.9
        b)  Approximately 0.4
        c)  Approximately 0.0
        d)  Approximately -0.4
        e)  Approximately -0.9

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2490-4

    Q:  In a given group, the correlation between height measured in feet and
        weight measured in pounds is +.68.  Which of the following would alter
        the value of r?
        a.  height is expressed centimeters.
        b.  weight is expressed in Kilograms.
        c.  both of the above will affect r.
        d.  neither of the above changes will affect r.

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2491-2

    Q:  The sign (plus or minus) of a correlation coefficient indicates
        a.  the direction of the relationship.
        b.  the practical importance of the relationship.
        c.  the probability that the degree of relationship is greater than
            zero.
        d.  the statistical significance of the relationship.

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2491-3

    Q:  The correlation between scores on a neuroticism test and scores on an
        anxiety test is high and positive; therefore
        a.  anxiety causes neuroticism.
        b.  those who score low on one test tend to score high on the other.
        c.  those who score low on one test tend to score low on the other.
        d.  no prediction from one test to the other can be meaningfully made.

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2492-2

    Q:  In correlational analysis, when the points scatter widely about the
        regression line, this means that the correlation is
        a.  negative.
        b.  low.
        c.  heterogeneous.
        d.  between two measures that are unreliable.

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2494-1

    Q:  Explain what correlation coefficients of -1, 0 and 1 mean, using
        graphs to illustrate.  What is the accuracy of prediction in each
        of these three cases given by YHAT = a + b*X and why?

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2503-2

    Q:  Body weight (pounds) was correlated with an exercise variable (as
        measured by Balke Treadmill Test) on n=14 college men.  If an r=0.01
        was obtained, what conclusions might be drawn?

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2504-1

    Q:  If one obtained an r = -.23 between wrestling ability and performance
        on a 50 yd. sprint run when testing 30 individuals, then one would be
        just as well off in prediction by just "flipping a coin" for each per-
        son to determine wrestling ability.  EXPLAIN THIS STATEMENT.

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2505-1

    Q:  Write an interpretation of each of the following correlations:

        a)  GIVEN:  r(X,Y) = -.68

               X = New York State Endurance Test
               Y = Fleishman's 600 yd. run
           Group = 11 college PE majors

        b)  GIVEN:  r(X,Y) = .255

               X = speed of movement: foot reaction time
               Y = speed of movement: sprint running
           Group = 32 college PE majors

        c)  GIVEN:  r(X,Y) = .00

               X = standing height
               Y = flexibility (trunk twist)
           Group = 25 college PE majors

        d)  GIVEN:  r(X,Y) = .902

               X = right grip strength
               Y = left grip strength
           Group = 25 college PE majors

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2513-1

    Q:  Discuss briefly the distinction between correlation and causality.

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2514-4

    Q:  True or False?

        If r is close to + or -1, we shall say there is a strong correlation,
        with the tacit understanding that we are referring to a linear rela-
        tionship and nothing else.

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2515-1

    Q:  True or False?  If false, correct it.

   If we know that the simple linear correlation coefficient is positive
        for pairs of observations (X(i),Y(i)), then geometrically speaking the
        regression of Y on X yields a regression line  that  slopes downward
        going from left to right.

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2515-3

    Q:  True or False?  If false, correct it.

        A correlation coefficient, r, measures the strength of the linear rela-
        tionship between variables and is proof of a cause-effect relationship
        between the variables.

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2516-1

    Q:  True or False?

        It  is  safer  to  interpret  correlation coefficients as measures of
        association rather than  causation  because  of  the  possibility  of
        spurious correlation.

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2516-2

    Q:  True or False?

        Whenever r is calculated on the basis of a sample, the value which we
        obtain for r is only an estimate of the true correlation coefficient
        which we would obtain if we calculated it for the entire population.

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2518-3

    Q:  Define the following term and give an example of its use.
        Your example should not be one given in class or in a handout.

        Correlation Coefficient

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2519-1

    Q:  Define the following term and give an example of its use.
        Your example should not be one given in class or in a handout.


        Simple Correlation or Simple Regression

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2524-1

    Q:  A sample survey was conducted to study the relationship between
        education and residence.  The following data were collected:

                               No. of Persons      Mean Number of Years
                Residence         in Sample         of School Completed

                  Urban               40                   11
                  Rural               40                    9

        a)  Complete the following Analysis of Variance Table for this
            data:

            Source of
            Variation              df      SS      MS      F

            Among Residences        1      80      __      __
            Within Residences      78     390      __
            Total                  79     470

        b)  What hypothesis does the above F-value test?

        c)  What do you conclude?  Give the proper F-value from the
            table for ALPHA = .05.

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2532-1

    Q:  Thirty patients in a leprosorium were randomly selected to be treated
        for several months with one of the following:

        A - an antibiotic
        B - a different antibiotic
        C - an inert drug used as a control

        At the end of the test period, laboratory tests were conducted to
        provide a measure of abundance of leprosy bacilli in each patient.

        Scores obtained were:

                Patient  1    2    3    4    5    6    7    8    9    10
        Drug A           6    0    2    8   11    4   13    1    8     0
        Drug B           0    2    3    1   18    4   14    9    1     9
        Drug C          13   10   18    5   23   12    5   16    1    20

            Analyze and interpret the results of this trial assuming that
            a oneway ANOVA already rejected the null hypothesis that all 
            drugs are equal. (use ALPHA = .05).
            Using the program CARROT*** you get the following results:

            Means for Antibiotics
            Treatment        Mean (leprosy bacilli)
            Placebo          12.3
            Drug A            5.3
            Drug B            6.1

            Tukey's HSD (at ALPHA = .05) = 5.57113

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2545-1

    Q:  Individual statistical comparisons between pairs of means
        in an analysis of variance must be preceded by:

        a.  a demonstrated significant correlation between the means
        b.  a significant over-all F value
        c.  neither of the above
        d.  both of the above

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Answers:

1148-2

    A:  d.  measures of traits A and B on each subject in one group

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1426-3

    A:  False.  Since H(O):  BETA = -1 would not be rejected at ALPHA = 0.05,
        it would not be rejected at ALPHA = 0.01.

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1526-1

    A:  a.  The population value for BETA(2), the change that occurs in Y
            with a unit change in X(2), when the other variables are held
            constant.

        b.  The population value for the standard error of the distribution
            of estimates of BETA(2).

        c.  .8, .1, 16 = 20 - 4.

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1543-1

    A:  a.  -.72, .32
        b.  the t value
        c.  the t value

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1656-2

    A:  True.

        t(critical, df = 23, two-tailed, ALPHA = .02) = +/- 2.5
        t(critical, df = 23, two-tailed, ALPHA = .01) = +/- 2.8

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1726-1

    A:  d.  YHAT = -15 dollars, which is obvious nonsense.  This reminds us
            that predicting Y outside the range of X values in our data is a
            very poor practice.

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1731-1

    A:  I would recommend only 3 coins because not having any observations over
        3 coins, I have no idea what may happen when extrapolating.  Another
        factor may enter the problem at higher levels that may be very
        unpleasant.  Don't forget that kings can be very nasty people, liable to
        chop off heads as their whims take them.

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1732-1

    A:  a.  80 + 1.5*4 = 86
        b.  No. I would not want to extrapolate that far.  If I did, my estimate
            would be 110, but some other factors probably come into play with
            20 years.

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1733-1

    A:  The precision of the estimate of the  Y variable depends on the range of
        the independent (X) variable explored.  If we explore a very small range
        of the X variable, we won't be able to make much use  of the regression.
        Also, extrapolation is not recommended.

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1738-1

    A:  Definition:     The act of making an estimate of response outside the
                        observed range of the independent variable or outside
                        the observed region of a set of independent variables.
                        This is usually regarded as a dangerous pasttime.

        Example:        Suppose that relative sobriety has been observed for
                        some person at various times after consumption of 1/10,
                        2/10, and 3/10 of some alcoholic drink.  Suppose that
                        the relation between relative sobriety and number of
                        drinks is described exactly by a straight line:
                        Sobriety(i) = 1.0 - .01 X(i), (X(i) = no. of drinks).
                        If we use this relation to estimate relative sobriety
                        for less than 1/10 drink or more than 3/10 drink, we
                        will have indulged in extrapolation.  e.g.  If we ask
                        what will be relative sobriety after 5 drinks, the above
                        expression says that it will be .95 (95% of sobriety
                        when no drinks have been consumed).  This may or may
                        not be a reasonable estimate depending on how well
                        reaction in the range 1/10 to 3/10 agrees with what
                        happens around 5.  Many would suspect substantial
                        disagreement in this case.

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1739-1

    A:  Definition:     The act of making an estimate of response within the
                     observed range of the independent variable or within
                        the observed region of a set of independent variables.
                        While this is usually regarded as a reasonably safe
                        undertaking, it should be noted that there have been
                        some famous cases where responses show irregular
                        behavior that is most disrespectful of interpolation.

        Example:        Suppose that relative sobriety has been observed for
                        some person at various times after consumption of 1,2,3,
                        and 5 portions of some alcoholic beverage.  Suppose that
                        the observed responses agree perfectly with

                             Sobriety(i) = 1.0 - .01X(i) - .01X(i)**2
                             (X(i):  no. of drinks)

                        If we ask what will be sobriety at 4 drinks, we obtain
                        estimated sobriety as 1.0 - .01(4) - .01(16) = .8.
                        The process of obtaining this estimate is called inter-
                        polation.  While it is regarded as much less dangerous
                        than extrapolation, it too can go awry if there are
                        peculiar squiggles in the true relation between
                        sobriety and number of drinks around 4 drinks.

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1751-1

    A:  a.  119
        b.  9
        c.  7+9+1+5+2=24
        d.  49+81+1+25+4=160
        e.  1.  YHAT(4) = 15 + (10*5) = 65
            2.  108 - 65 = 43
            3.  j    e(j)    e(j)**2
                1     16        256
                2     14        196
                3     96       9216
                4     43       1849
                5     77       5929
                SUM (e(j)**2) = 17446

        f.    Y |
                |
                |    *
            120 +
                |                                            *
                |
                |
                |
            115 +
                |
                |
                |         *
                |
            110 +
                |
                |                        *
                |
                |
            105 +
                |
                |
                |
                |                                  *
            100 +
                |
               /

                |
                -----+----+----+----+----+----+----+----+----+------> X
                     1    2    3    4    5    6    7    8    9

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1753-1

    A:          N =   4

        Plotting Points:
            YHAT(A) = -.65 + 2.2(1) = 1.55;     Pt. A (1,1.5)
            YHAT(B) = -.65 + 2.2 (3.5) = 7.05;  Pt. B (3.5,7)


               |
               |
             8 +                               x
               |
             7 +                           B
               |
             6 +                       x
               |
          Y  5 +
               |
             4 +
               |
             3 +
               |
             2 +       x
               |       A
             1 +
               |
             0 ----+---+---+---+---+---+---+---+---+---+---+---+--->
               |       1       2       3       4       5       6
            -1 x                       X
               |
               |

               Note:   - Connect points A and B with a straight line to
                         obtain the graph of the regression line.
                       - x denotes points in the data set.

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1755-1

    A:  a.
                                       Y

                                       - 4
                                       |
                                       |
                   x                   - 3
                                       |
                                       |
                                  x    - 2
                                       |
                                       |
                                       - 1
                                       |
                                       |
            -------|----|----|----|----|----|----|----|----|-----------  X
                  -4   -3   -2   -1    |0   1    2    3    4
                                       |
                                       - -1     x
                                       |
                                       |
                                       - -2
                                       |
                                       |
                                       - -3
                                       |
                                       |
                                       - -4          x


        b. This means that 87.1% of the variation in the Y variable is
            explained by the X variable.

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1757-1

    A:  Scatterplot:

              |
              |
           12 +
              |
           11 +
              |
           10 +
              |
            9 +
         Y    |
            8 +
              |
            7 +                                                           x
              |
            6 +                                                           B
              |
            5 +
              |
            4 +                                                      x
              |
            3 +
              |
            2 +                                       x         x
              |
            1 +
              |
              -----+----+----+----+----+----+----A----+----+----+----+----+-->
              0    1    2    3    4    5    6    7    8    9   10   11   12
                                         X

        NOTE:  - x indicates data points.
               - connect points A and B with a straight line to get
                 an approximation of the regression line.

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1762-2

    A:  True.

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1763-1

    A:  Definition:     A graph in which values of one variable (i.e. X) are
                        plotted against corresponding values of another vari-
                        able (i.e. Y).

        Example:        Suppose that a data set is:

                                Happiness (Y)   No. of Wives (X)

                                    10                  0
                                     7                  1
                                     5                  2
                                     8                  1
                                     7                  2
                                     4                  3
                                     9                  0

                        Scatter diagram for this set is:

                                   |
                                 Y |
                                   |
                                10 x
                        Happiness  |
                                 9 x
                                   |
                                 8 +   x
                                   |
                                 7 +   x   x
                                   |
                                 6 +
                                   |
                                 5 +       x
                                   |
                                 4 +           x
                                   |


                                   |
                        ----+---+---+---------------------> X
                                   0   1   2   3
                                               No. of Wives

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1861-3

    A:  c)  16%

            (-.4)**2 = .16 or 16 percent

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1991-1

    A:  a.  Y(j) = b(0) + b(1)*X(j) + e(j)
        b.  Y(j) = b(0) - b(1)*X(j) + e(j)
        c.  Y(j) = YBAR + e(j)
        d.  Y(j) = b(0) + b(1)*X(j) + b(11)*X(j)**2 + b(111)*X(j)**3 + e(j)
        e.  Y(j) = b(0) + b(1)*X(j) + b(11)*X(j)**2 + e(j)

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1993-1

    A:  Y(j) = b(0) + b(1)*X(1) + b(2)*X(2) + b(3)*X(3) + b(4)*X(4) + b(5)*X(6)
               + e(j)

        where the dependent variable is variable 5 - miles per gallon and the
        independent variables are
                X(1) - miles driven per day
                X(2) - weight of car
                X(3) - number of cylinders in car
                X(4) - average speed
                X(6) - number of passengers

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1994-1

    A:  Y = B(0) + B(1)*X(2) + B(2)*X(3) + B(3)*X(5)

        where Y is the estimated response - % alcohol in blood
        and the independent variables are
                X(2) - number of drinks consumed
                X(3) - weight
                X(5) - time spent in consuming drinks

        I have excluded sex from my proposed model because I don't think it
        would have much of an effect on the percent of alcohol in blood.

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2088-1

    A:  YHAT = -3.6 + (3.1 * 7)
                 = 18.1

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2091-1

    A:  Most simply, since -5 is included in the confidence interval for the
        slope, we can conclude that the evidence is consistent with the claim
        at the 95% confidence level.

        Using a t test:         H(O):  B(1) = -5
                                H(A):  B(1) =/= -5

        t(calculated) = (-5 - (-4))/1 = -1
        t(critical) = -1.96

        Since t(calc) < t(crit) we retain the null hypothesis that B(1) = -5.

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2123-1

    A:  a.  Around 12,500 dollars per year.

        b.  There appears to be approximately a straight line relation in which
            income increases with experience over the interval  from  0  to 20.
            (There seems to be some curvature or flattening for experience near
            20.)  The change in income in this range  is  from  around 12.5  to
            around 48, so the rate of increased income is roughly $35,500/20   =
            $1775 per year.

        c.  The relation between experience and income  for experience  between
            20 and 30 years also appears to be roughly a straight line,  but  a
            flat straight line, indicating that income stays  roughly  constant
            at a little less than $50,000 per year.

        d.  The overall graph indicates income initially around $12,500 (no ex-
            perience), increasing income in the range from 0 to 20 years exper-
            ience, approaching a limit that seems to be a little below $50,000.
            That limit seems to be reached sometime between 10 and 25 years.
            (Income seems to remain about constant afterward.)

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2135-1

    A:  Definition:  A t test is obtained by dividing a regression coefficient
                     by its standard error and then comparing the result to
                     critical values for Students' t with Error df.  It provides
                     a test of the claim that BETA(i) = 0 when all other
                     variables have been included in the relevant regression
                     model.

        Example:     Suppose that 4 variables are suspected of influencing
                     some response.  Suppose that the results of fitting:
                     Y(i) = BETA(0) + BETA(1)X(1i) + BETA(2)X(2i) + BETA(3)
                                X(3i) + BETA(4)X(4i) + e(i) include:
                     Variable    Regression coefficient    Standard error of
                                                                reg. coef.
                        1               -3                        .5
                        2               +2                        .4
                        3               +1                        .02
                        4               -.5                       .6
                     t calculated for variables 1, 2, and 3 would be 5 or
                     larger in absolute value while that for variable 4 would be
                     less than 1.  For most significance levels, the hypothesis
                     BETA(1) = 0 would be rejected.  But, notice that this is
                     for the case when X(2), X(3), and X(4) have been included
                     in the regression.  For most significance levels, the
                     hypothesis BETA(4) = 0 would be continued (retained) for
                     the case where X(1), X(2), and X(3) are in the regression.
                     Often this pattern of results will result in computing
                     another regression involving only X(1), X(2), X(3), and
                     examination of the t ratios produced for that case.

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2138-2

    A:  c.  .025

            F(critical, df = 1,12, ALPHA = .025) = 6.55
            F(critical, df = 1,12, ALPHA = .01)  = 9.33

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2443-1

    A:  b.  74/86

            Coeff. of Mult. Det. = explained variation / total variation
                                 = SUM((Y(est) - YBAR)**2) / SUM((Y - YBAR)**2)
                                 = 74/86

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2443-2

    A:  d.  one quarter

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2444-2

    A:  b)  r = -.77

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2445-1

    A:  a.  81% of the variation in the money spent for repairs is explained
            by the age of the auto

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2445-2

    A:  a.  37%

            r = 0.61
            r**2 = .37 (coefficient of determination)

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2446-2

    A:  b.  16

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2449-1

    A:  True

        .7**2 = .49 = 49%.

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2449-2

    A:  False.

        The coefficient of determination is r**2 with 0 <= r**2 <= 1,
        since -1 <= r <= 1.

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2449-3

    A:  False, the sample correlation coefficient squared (r**2) is the pro-
        portion of variation in Y which is explained by Y's linear dependence
        on X.

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2469-1

    A:  b.  The linear relation between X and Y is strong, and Y decreases
            when X increases.

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2470-1

    A:  c.  The statistician is right,  because the correlation measures  how
            much linear relationship there is,  and  the relationship is cer-
            tainly not linear.

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2471-2

    A:  d.  there is a perfect negative relationship between Y and X in the
            sample.

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2471-3

    A:  a)  the correlation coefficient.

            Of these four tests only the correlation coefficient gives a
            measure of the relationship between variables.

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2472-1

    A:  b)  strong and positive

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2473-1

    A:  b.  negatively related

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2474-1

    A:  b.  increases in Variable A are accompanied by decreases in Variable B.

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2475-1

    A:  b.  as performance on complex tasks improves, anxiety tends to decrease.

            (c.) is objectionable because of the word "cause".  Correlation
            alone does not support "cause and effect" relationships.

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2475-2

    A:  a.  individuals scoring high on one variable tend to score low
            on the other variable.

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2476-1

    A:  b.  they should hire a new statistician.
            Correlation scores range from -1 to 1.

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2481-1

    A:  d.  on a scale from -1 to +1, the degrees of linear relationship between
            the two variables is +.10

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2481-3

    A:  c and e, since r**2 is greater that .5 in each case.

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2482-1

    A:  d.

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2484-1

    A:  d.  there exists no linear relationship between X and Y

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2486-1

    A:  a.  .4

            Correlation coefficient will remain the same.

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2487-2

    A:  d.  Variable Y tends to decrease as Variable X increases

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2487-4

    A:  b.  is the same degree of relationship as r=+.80

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2488-3

    A:  a)  Approximtely 0.9

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2490-4

    A:  d.  neither of the above changes will affect r.

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2491-2

    A:  a.  the direction of the relationship.

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2491-3

    A:  c.  those who score low on one test tend to score low on the other.

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2492-2

    A:  b.  low.

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2494-1

    A:
             |         r = 1
             |
             |              *
             |
             |           *
             |
         Y   |        *
             |
             |
             |    *
             |
             |*
             ------------------------->
                         X
        (Connect the points to form a straight line.)

        If X is one variable and Y the other, when r=1 we have all ordered
        pairs (X,Y) on a straight line as shown.  Thus, as one variable
        increases, the other does also in such a way that each ordered pair
        (X,Y) of values lies on the line.  This is the strongest possible
        direct relationship.

             |         r = -1
             |
             |*
             |
             |    *
             |
             |        *
          Y  |
             |            *
             |
             |                *
             |
             |                    *
             --------------------------->
                           X
        (Connect the points to form a straight line.)

        When r=-1, we have all ordered pairs on a straight line as shown.
        Thus, as one variable increases, the other decreases in such a way
        that each ordered pair (X,Y) of values lies on a line.  This is the
        strongest possible inverse relationship.

             |        r = 0
             |
             |    *      *  *
             |*      *        *
             |     *    *
             |      *    **
          Y  |  *     *      *
             | *   **      *
             |
             |      **    ****
             |  *      *      *
             |**   **   * * *
             ----------------------->
                        X

        When r=0, there is no linear relationship between X and Y.  The points
        have no linear pattern.

        The formula given predicts Y given X perfectly if r=-1 or r=1 and
        extremely poorly if r=0.  The closer to 1 or -1 r is, the better a
        predictor of Y given by the formula.

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2503-2

    A:  No information is provided on diet, so no conclusions can be drawn.

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2504-1

    A:  An r value of -.23 is so small that it would probably not prove to
        be significant.  Therefore, one can assume that there is no corre-
        lation between wrestling ability and time to run a 50 yd. sprint.
        The 50 yard sprint is as poor in predicting wrestling ability as is
        flipping a coin for each person to determine wrestling ability.

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2505-1

    A:  a)  The moderately high inverse correlation between X and Y suggests
            that PE majors who score high on the New York State Endurance Test
            tend to complete the 600 yd. run in less time.

        b)  The correlation coefficient is positive but weak.  Therefore, one
            can conclude that there is little relationship between speed of
            movement: foot reaction time and speed of movement: sprint running
            for PE majors.

        c)  Since r = 0, there is no relationship between standing height and
            flexibility (trunk twist) for PE majors.

        d)  The high, positive correlation coefficient suggests a strong
            relationship between right grip strength and left grip strength
            for PE majors.

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2513-1

    A:  Some variables seem to be related,  so  that  knowing  one  variable's
        status   allows  us  to  predict  the  status  of  the  other.  This
        relationship can be measured and is  called  correlation.  However,  a
        high  correlation between two variables in no way proves that a cause
        and effect relation exists between them. It is entirely possible that
        a third factor causes both variables to vary together.

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2514-4

    A:  True

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2515-1

    A:  False, it slopes upward going from left to right.

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2515-3

    A:  False, it does not provide any proof of a cause-effect relationship.

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2516-1

    A:  True

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2516-2

    A:  True

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2518-3

    A:  Definition:     A measure of the degree to which variation of one
                        variable is related to variation in one or more
                        other variables.  The most commonly used correlation
                        coefficient indicates the degree to which variation
                        in one variable is described by a straight line
                        relation with another variable.

        Example:        Suppose that sample information is available on
                        Family income and Years of schooling of the head
                        of the household.  A correlation coefficient = 0
                        would indicate no linear association at all between
                        these two variables.  A correlation of 1 would indicate
                        perfect linear association (where all variation in
                        family income could be associated with schooling and
                        vice versa).

        Symbol:         r

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2519-1

    A:  Definition:     Correlation or regression involving two variables -
                        one of which may be regarded as dependent and one
                        which may be regarded as independent.

        Example:        Suppose that we collect data on the height, weight,
                        and a number of additional characteristics of 100
                        college students.  If we calculate a correlation
                        using just the data for height and weight, that
                        correlation is called a simple correlation.  If we
                        calculate a regression of, say, weight on height,
                        that regression is called a simple regression.

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2524-1

    A:  a)  Source of
            Variation              df      SS      MS      F

            Among Residences        1      80      80      16
            Within Residences      78     390       5
            Total                  79     470

        b)  H(0):  MU(1) = MU(2)

            or no difference in mean number of years of school completed
            by residences.

        c)  F(critical, df = 1, 78, ALPHA = .05, onetail) == 3.96

            Reject H(0) and conclude that difference is significant with
            urban residents having a higher mean number of years of
            school.

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2532-1

    A:     HSD tests on means:

                H(0):  XBAR(1) - XBAR(2) = 0
                H(A):  XBAR(1) - XBAR(2) =/= 0

            (XBAR(1) - XBAR(2)) +/- HSD
            Placebo and drug B

            6.2 +/- 5.57
            Interval is from +.63 to +11.77

            The interval does not contain zero, therefore, we reject H(0).

            Since both antibiotic treatments are significantly different from
            the placebo, one would conclude that they have a significant effect
            on reducing leprosy bacilli.  However, antibiotics A and B are not
            significantly different from each other.  The differences in their
            means could be attributed to chance variation alone.

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2545-1

    A:  b.  a significant over-all F value

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Return to Brian Schott @ GSU

Identification:

1148-2

Item is still being reviewed
        Multiple Choice
EXPERDESIGN/TERM  DESIGN            CONCEPT
        CORRELATION/P     ANOVA             PARAMETRIC
        STATISTICS

T= 2    Comprehension
D= 1    General

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1426-3

Item is still being reviewed
        True/False
SIMPLE/REG        CONFIDENCEINTERV  TESTOFSIGNIFICAN
        REGRESSION        PARAMETRIC        STATISTICS
        ESTIMATION        CONCEPT

T= 2    Comprehension
D= 5    General

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1526-1

Based upon item submitted by A. Bugbee - UNH
        Fill-in
MULTIPLE/REG      OTHER/CI          STANDERROR/OTHER
        REGRESSION        PARAMETRIC        STATISTICS
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        DESCRSTAT/P

T= 5    Computation     Comprehension
D= 3    General
                ***Multiple Parts***

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1543-1

Based upon item submitted by J. Warren - UNH
        Short Answer
MULTIPLE/REG      OTHER/CI
        MODEL             DEGREESOFFREEDOM  I650A
        REGRESSION        PARAMETRIC        STATISTICS
        CONFIDENCEINTERV  ESTIMATION        CONCEPT
        ANOVA

T= 5    Computation     Comprehension
D= 5    General
                ***Multiple Parts***

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1656-2

Based upon item submitted by D. Kleinbaum - Univ of North Carolina
        True/False
TESTOFSIGNIFICAN  TWOTAIL/T         SIMPLE/REG
        CONCEPT           STATISTICS        TTEST
        PARAMETRIC        REGRESSION

T= 2    Comprehension
D= 4    General
                ***Statistical Table Necessary***

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1726-1

Item is still being reviewed
        Multiple Choice
SCOPEOFINFERENCE  SIMPLE/REG
        CONCEPT           STATISTICS        REGRESSION
        PARAMETRIC

T= 5    Comprehension
D= 3    General             Business

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1731-1

Item is still being reviewed
        Short Answer
OTHER/REG         SCOPEOFINFERENCE
        COMMONPITFALLS    I650A             REGRESSION
        PARAMETRIC        STATISTICS        CONCEPT

T= 5    Comprehension
D= 4    General

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1732-1

Based upon item submitted by J. Warren - UNH
        Short Answer
SIMPLE/REG        SCOPEOFINFERENCE
        MODEL             I650A             REGRESSION
        PARAMETRIC        STATISTICS        CONCEPT

T= 5    Comprehension   Computation
D= 4    Natural Sciences    Biological Sciences
                ***Multiple Parts***

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1733-1

Based upon item submitted by J. Inglis
        Short Answer
SIMPLE/REG        SCOPEOFINFERENCE
        REGRESSION        PARAMETRIC        STATISTICS
        CONCEPT

T= 2    Comprehension
D= 3    General

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1738-1

Based upon item submitted by J. Warren - UNH
        Definition
BASICTERMS/REG    SCOPEOFINFERENCE
        RANGE             I650A             REGRESSION
        PARAMETRIC        STATISTICS        CONCEPT
        VARIABILITY/NP    DESCRSTAT/NP      NONPARAMETRIC

T= 5    Comprehension
D= 3    General

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1739-1

Based upon item submitted by J. Warren - UNH
        Definition
BASICTERMS/REG    SCOPEOFINFERENCE
        I650A             REGRESSION        PARAMETRIC
        STATISTICS        CONCEPT

T= 5    Comprehension
D= 3    General

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1751-1

Based upon item submitted by J. Warren - UNH
        Numerical Answer
SIMPLE/REG        SCATDIAGRAM/P
        I650A             REGRESSION        PARAMETRIC
        STATISTICS        DESCRSTAT/P

T= 5    Comprehension
D= 3    General
                ***Multiple Parts***

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1753-1

Item is still being reviewed
        Numerical Answer
SCATDIAGRAM/P     SIMPLE/REG        SIMPLE/COR
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        REGRESSION        CORRELATION/P

T=15    Computation
D= 5    General

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1755-1

Item is still being reviewed
        Numerical Answer
SCATDIAGRAM/P     SIMPLE/COR        COEFFDETERMINAT
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        CORRELATION/P     REGRESSION

T=10    Computation     Comprehension
D= 5    General
                ***Calculator Necessary***
                ***Graph or Chart Necessary***
                ***Multiple Parts***

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1757-1

Item is still being reviewed
        Numerical Answer
SCATDIAGRAM/P     SIMPLE/REG
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        REGRESSION

T=15    Computation
D= 5    General
                ***Calculator Necessary***
                ***Graph or Chart Necessary***

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1762-2

Item is still being reviewed
        True/False
SCATDIAGRAM/P
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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1763-1

Item is still being reviewed
        Definition
SCATDIAGRAM/P
        I650A             DESCRSTAT/P       PARAMETRIC
        STATISTICS

T= 5    Comprehension
D= 3    General

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1861-3

Item is still being reviewed
        Multiple Choice
SIMPLE/COR        VARIABILITY/P
        CORRELATION/P     PARAMETRIC        STATISTICS
        DESCRSTAT/P

T= 2    Computation
D= 3    Psychology          General

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1991-1

Based upon item submitted by J. Warren - UNH
        Short Answer
MODEL             OTHER/REG         POPULATIONMODELS
        TYPICALPIC/GRAPH  I650A             REGRESSION
        PARAMETRIC        STATISTICS        DESCRSTAT/P

T= 5    Comprehension
D= 3    General
                ***Multiple Parts***

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1993-1

Item is still being reviewed
        Short Answer
MULTIPLE/REG      POPULATIONMODELS
        MODEL             I650A             REGRESSION
        PARAMETRIC        STATISTICS        DESCRSTAT/P

T=10    Comprehension
D= 4    General             Natural Sciences

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1994-1

Based upon item submitted by J. Warren - UNH
        Short Answer
MULTIPLE/REG      POPULATIONMODELS
        MODEL             I650A             REGRESSION
        PARAMETRIC        STATISTICS        DESCRSTAT/P

T= 5    Application
D= 4    Biological Sciences General

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2088-1

Item is still being reviewed
        Numerical Answer
VARIANCE/OTHER    SIMPLE/REG        STANDERROR/OTHER
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        REGRESSION

T= 2    Application     Computation
D= 2    Biological Sciences General
                ***Calculator Necessary***

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2091-1

Based upon item submitted by J. Warren - UNH
        Short Answer
SIMPLE/REG        TWOTAIL/T         STANDERROR/OTHER
        I650A             REGRESSION        PARAMETRIC
        STATISTICS        TTEST             DESCRSTAT/P
        TESTOFSIGNIFICAN  CONCEPT

T=10    Application
D= 6    General
                ***Statistical Table Necessary***

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2123-1

Item is still being reviewed
        Short Answer
GRAPH/PICTOGRAPH
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T=10    Comprehension
D= 2    General             Economics           Business
                ***Multiple Parts***

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2135-1

Based upon item submitted by J. Warren - UNH
        Definition
REGRESSION        TTEST
        I650A             PARAMETRIC        STATISTICS

T= 5    Comprehension
D= 4    General

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2138-2

Item is still being reviewed
        Multiple Choice
SIMPLE/REG
        FTEST             PARAMETRIC        STATISTICS
        REGRESSION

T= 5    Comprehension
D= 5    General
                ***Statistical Table Necessary***

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2443-1

Item is still being reviewed
        Multiple Choice
COEFFDETERMINAT
        REGRESSION        PARAMETRIC        STATISTICS

T=10    Computation
D= 6    General

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2443-2

Item is still being reviewed
        Multiple Choice
SIMPLE/COR        COEFFDETERMINAT
        CORRELATION/P     PARAMETRIC        STATISTICS
        REGRESSION

T= 2    Comprehension
D= 3    General

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2444-2

Item is still being reviewed
        Multiple Choice
SIMPLE/COR        COEFFDETERMINAT
        CORRELATION/P     PARAMETRIC        STATISTICS
        REGRESSION

T= 2    Comprehension
D= 3    General

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2445-1

Item is still being reviewed
        Multiple Choice
COEFFDETERMINAT   SIMPLE/COR
        REGRESSION        PARAMETRIC        STATISTICS
        CORRELATION/P

T= 2    Comprehension
D= 2    General

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2445-2

Item is still being reviewed
        Multiple Choice
COEFFDETERMINAT
        REGRESSION        PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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2446-2

Item is still being reviewed
        Multiple Choice
COEFFDETERMINAT
        REGRESSION        PARAMETRIC        STATISTICS

T= 2    Comprehension   Computation
D= 4    General             Education           Psychology

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2449-1

Item is still being reviewed
        True/False
SIMPLE/COR        COEFFDETERMINAT
        CORRELATION/P     PARAMETRIC        STATISTICS
        REGRESSION

T= 2    Comprehension
D= 3    General

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2449-2

Item is still being reviewed
        True/False
SIMPLE/COR        COEFFDETERMINAT
        CORRELATION/P     PARAMETRIC        STATISTICS
        REGRESSION

T= 2    Computation
D= 2    General

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2449-3

Item is still being reviewed
        True/False
COEFFDETERMINAT   CORRELATION/P
        REGRESSION        PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 5    General

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2469-1

Item is still being reviewed
        Multiple Choice
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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2470-1

Based upon item submitted by F. J. Samaniego - UC Davis
        Multiple Choice
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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2471-2

Based upon item submitted by A. Bugbee - UNH
        Multiple Choice
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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2471-3

Based upon item submitted by R. Shavelson - UCLA
        Multiple Choice
SIMPLE/COR
        ANOVA             TTEST             CORRELATION/P    
        PARAMETRIC        STATISTICS        NONPARAMETRIC

T= 5    Comprehension
D= 4    General             Education           Psychology

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2472-1

Based upon item submitted by W. Dixon - UCLA
        Multiple Choice
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    Psychology

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2473-1

Based upon item submitted by R. Shavelson - UCLA
        Multiple Choice
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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2474-1

Based upon item submitted by R. Shavelson - UCLA
        Multiple Choice
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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2475-1

Based upon item submitted by R. Shavelson - UCLA
        Multiple Choice
SIMPLE/COR
        I650A             CORRELATION/P     PARAMETRIC
        STATISTICS

T= 2    Comprehension
D= 3    Psychology

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2475-2

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Multiple Choice
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 1    General

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2476-1

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Multiple Choice
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 1    General

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2481-1

Item is still being reviewed
        Multiple Choice
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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2481-3

Based upon item submitted by J. Warren - UNH
        Multiple Choice
SIMPLE/COR
        I650A             CORRELATION/P     PARAMETRIC
       STATISTICS

T= 2    Comprehension
D= 3    General

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2482-1

Based upon item submitted by J. Warren - UNH
        Multiple Choice
SIMPLE/COR
        I650A             CORRELATION/P     PARAMETRIC
        STATISTICS

T= 2    Comprehension
D= 3    General

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2484-1

Based upon item submitted by J. Inglis
        Multiple Choice
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 4    General

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2486-1

Based upon item submitted by J. Inglis
        Multiple Choice
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 3    General

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2487-2

Item is still being reviewed
        Multiple Choice
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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2487-4

Item is still being reviewed
        Multiple Choice
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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2488-3

Item is still being reviewed
        Multiple Choice
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    Business            Economics

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2490-4

Item is still being reviewed
        Multiple Choice
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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2491-2

Item is still being reviewed
        Multiple Choice
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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2491-3

Item is still being reviewed
        Multiple Choice
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    Psychology          General

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2492-2

Item is still being reviewed
        Multiple Choice
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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2494-1

Based upon item submitted by J. Mowbray - Shippensburg State
        Essay
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T=10    Comprehension
D= 2    General

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2503-2

Based upon item submitted by K. Amsden - UNH
        Short Answer
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    Education

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2504-1

Based upon item submitted by K. Amsden - UNH
        Short Answer
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    Biological Sciences Education           General

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2505-1

Based upon item submitted by K. Amsden - UNH
        Short Answer
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 5    Comprehension
D= 2    Education
                ***Multiple Parts***

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2513-1

Item is still being reviewed
        Short Answer
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 5    Comprehension
D= 4    General

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2514-4

Item is still being reviewed
        True/False
SIMPLE/COR
        MODEL             CORRELATION/P     PARAMETRIC
        STATISTICS        MISCELLANEOUS

T= 2    Comprehension
D= 2    General

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2515-1

Based upon item submitted by B. Bosworth - St. John's Univ.
        True/False
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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2515-3

Based upon item submitted by B. Bosworth - St. John's Univ.
        True/False
SIMPLE/COR
        MODEL             ASSUMPTCUSTOMARY  CORRELATION/P
        PARAMETRIC        STATISTICS        MISCELLANEOUS

T= 2    Comprehension
D= 2    General

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2516-1

Based upon item submitted by B. Bosworth - St. John's Univ.
        True/False
SIMPLE/COR
        CORRELATION/P     PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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2516-2

Item is still being reviewed
        True/False
SIMPLE/COR
        SAMPLE            SAMPDIST/C        CORRELATION/P
        PARAMETRIC        STATISTICS        SAMPLING
        ESTIMATION        CONCEPT

T= 2    Comprehension
D= 2    General

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2518-3

Based upon item submitted by J. Warren - UNH
        Definition
SIMPLE/COR
        I650A             CORRELATION/P     PARAMETRIC
        STATISTICS

T= 5    Comprehension
D= 3    General

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2519-1

Based upon item submitted by J. Warren - UNH
        Definition
SIMPLE/COR
        I650A             CORRELATION/P     PARAMETRIC
        STATISTICS

T= 5    Comprehension
D= 2    General

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2524-1

Based upon item submitted by A. Bugbee - UNH
        Short Answer
FTEST             ANOVA
        PARAMETRIC        STATISTICS

T=10    Application
D= 4    Social Sciences     General
                ***Multiple Parts***
                ***Statistical Table Necessary***

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2532-1

Based upon item submitted by J. Warren - UNH
        Short Answer
COMPLETELYRANDOM  ANOVA             MULTIPLECOMPARIS
        MODEL             TYPICALSUMMARY    I650C
        PARAMETRIC        STATISTICS

T= 5    Application
D= 4    Biological Sciences General             Natural Sciences

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2545-1

Based upon item submitted by R. L. Stout & R. M. Paolino - Brown
        Multiple Choice
OTHER/AN          EXPERDESIGN/TERM
        ANOVA             PARAMETRIC        STATISTICS

T= 5    Comprehension
D= 6    General

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