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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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Q: True or false? If false, explain why. The coefficient of determination can have values between -1 and +1.

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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Q: Discuss briefly the distinction between correlation and causality.

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

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Look at this question's identification

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

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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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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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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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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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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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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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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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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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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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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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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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A: True.

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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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A: c) 16% (-.4)**2 = .16 or 16 percent

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

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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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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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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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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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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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A: d. one quarter

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A: b) r = -.77

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

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A: a. 37% r = 0.61 r**2 = .37 (coefficient of determination)

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A: b. 16

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A: True .7**2 = .49 = 49%.

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

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

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

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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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A: b) strong and positive

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A: b. negatively related

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

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

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

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

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

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A: d.

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

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A: a. .4 Correlation coefficient will remain the same.

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

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

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A: a) Approximtely 0.9

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

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A: a. the direction of the relationship.

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

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A: b. low.

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

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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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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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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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A: True

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

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

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A: True

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A: True

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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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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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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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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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A: b. a significant over-all F value

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Item is still being reviewed True/False COEFFDETERMINAT CORRELATION/P REGRESSION PARAMETRIC STATISTICS T= 2 Comprehension D= 5 General

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Item is still being reviewed Multiple Choice SIMPLE/COR CORRELATION/P PARAMETRIC STATISTICS T= 2 Comprehension D= 2 General

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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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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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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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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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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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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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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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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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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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Item is still being reviewed Multiple Choice SIMPLE/COR CORRELATION/P PARAMETRIC STATISTICS T= 2 Comprehension D= 2 General

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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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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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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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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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Item is still being reviewed Multiple Choice SIMPLE/COR CORRELATION/P PARAMETRIC STATISTICS T= 2 Comprehension D= 2 General

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Item is still being reviewed Multiple Choice SIMPLE/COR CORRELATION/P PARAMETRIC STATISTICS T= 2 Comprehension D= 2 Business Economics

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Item is still being reviewed Multiple Choice SIMPLE/COR CORRELATION/P PARAMETRIC STATISTICS T= 2 Comprehension D= 2 Psychology General

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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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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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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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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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Item is still being reviewed Short Answer SIMPLE/COR CORRELATION/P PARAMETRIC STATISTICS T= 5 Comprehension D= 4 General

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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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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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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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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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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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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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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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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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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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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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