Deck 5: Correlation and Regression

Question 1

In the following correlation matrix, which two exams correlate the highest, and which two correlate the lowest? $\begin{array}{lcccc} & \text { Exam 1 } & \text { Exam 2 } & \text { Exam 3 } & \text { Exam } \\\text { Exam 1 } & 1.00 & -.025 & -.740 & -.36 \\\text { Exam 2 } & -.025 & 1.00 & .425 & .011 \\\text { Exam 3 } & -.740 & .425 & 1.00 & .682 \\\text { Exam 4 } & -.366 & .011 & .682 & 1.00\end{array}$

A) Highest: Exam 1 & Exam 3; lowest: Exam 2 & Exam 4
B) Highest: Exam 3 & Exam 4; lowest: Exam 1 & Exam 2
C) Highest: Exam 1 & Exam 3; lowest: Exam 1 & Exam 2
D) Highest: Exam 3 & Exam 4; lowest: Exam 1 & Exam 3

Answer 1

Highest: Exam 1 & Exam 3; lowest: Exam 2 & Exam 4

Question 2

What does a correlation coefficient describe about the relationship between two variables?

A) The variability and strength
B) The variability and direction
C) The mean and variability
D) The direction and strength

Answer 2

D

Question 3

If there is a negative correlation between leg strength scores and the time to run a 50-yard dash, what run times are associated with high leg strength scores?

A) Slow times
B) Fast times
C) Either fast or slow times
D) It depends on the variability of the scores

Answer 3

B

Question 4

If the correlation coefficient between the length of marriage and marital happiness is +.82, what can we conclude?

A) Happiness declines as the number of years married increases
B) Short marriages are happy marriages
C) Happy marriages cause long marriages
D) Long marriages tend to be happy ones

Question 5

How much of the variance in final exam scores is accounted for by the variance in Exam 1's scores, if the coefficient between the two exams is .45?

A) .20
B) .45
C) .67
D) Depends on sample size

Question 6

What pattern of correlations would produce the best multiple regression equation?

Question 7

A simple regression formula for predicting weight in pounds from height in inches is Ŷ= 1.6X + 60. What is the slope of the regression line to predict weight from height?

A) 60
B) 61.6
C) 37.5
D) Positive

Question 8

Given that the regression equation is Ŷ = .5X + 25 and the standard error of estimate is 3, what is the range of scores that would capture a person's true Y score 68% of the time, if that person had an X score of 30?

A) 27-33
B) 37-43
C) 37-53
D) 34-46

Question 9

What is the standard deviation of the residuals resulting from predicting Y scores from X scores?

A) Zero
B) One
C) SEM
D) SEE

Question 10

If the regression equation Ŷ= .25X + 12 was plotted, what shape would it take, and where would it cross the Y axis?

A) Curvilinear, at Y=.25
B) Curvilinear, at Y=12
C) Linear, at Y=.25
D) Linear, at Y=12

Question 11

If two predictor variables to be used in developing a multiple regression equation both correlate with the criterion variable at .75, what correlation coefficient between the two predictor variables would lead to the most efficient regression equation?

A) .00
B) .25
C) .75
D) .95

Question 12

Which of the following is the primary purpose of correlational research?

A) To study individual situations in depth
B) To study disease rates in the population
C) To combine and quantify past research reports
D) To study the relationships among variables

Question 13

Which of the following statistics is a measure of the amount of variance accounted for between two variables?

A) Standard deviation
B) r²
C) r
D) SEE

Question 14

Which symbol is commonly used to indicate a Pearson product-moment correlation coefficient?

A) r
B) s
C) P
D) C

Question 15

What does a negative value of r mean?

A) There is no relationship between two variables
B) High scores on one variable are associated with low scores on a second variable
C) High scores on one variable are associated with high scores on a second variable
D) There is a mistake in the calculation of the coefficient

Question 16

What conclusion should be drawn if the correlation coefficient between a physical fitness test and a rating of basketball playing ability is .90?

A) People who are physically fit will be successful in playing basketball.
B) Playing basketball develops physical fitness.
C) Physical fitness is necessary to be successful in playing basketball.
D) Basketball playing ability and physical fitness are strongly associated.

Question 17

What does a correlation coefficient of +.91 mean?

A) No relationship exists between two variables.
B) Those who did better on the first test did worst on the second test.
C) Those who did better on the first test were average on the second test.
D) Those who did better on the first test also did better on the second test.

Question 18

Of the following, which correlation coefficient best describes the relationship between height and weight in healthy adults?

A) -.87
B) .00
C) +.10
D) +.45

Question 19

If a test of athletic ability has a .12 correlation coefficient with batting average in baseball, how well does the test predict batting success?

A) Extremely well
B) Very well
C) Moderately well
D) Not very well

Question 20

Which correlation method is used when both variables are measured on an ordinal level?

A) Pearson's r
B) Spearman's rho
C) Rank biserial
D) Point biserial

Question 21

Which statistical method is used to estimate percent body fat based on age, gender, and skinfold measurements?

A) Pearson's r
B) Spearman's rho
C) Simple regression
D) Multiple regression

Question 22

Using the following correlation matrix, assume that you want to use two of the tests to measure the criterion. Which two tests would you use? $\begin{array}{lcccc} & \text { Test A } & \text { Test B } & \text { Test C } & \text { Criterion } \\\text { TestA } & 1.00 & .56 & .25 & .75 \\\text { TestB } & & 1.00 & .25 & .00 \\\text { TestC } & & & 1.00 & .50\end{array}$

A) Test A and Test B
B) Test A and Test C
C) Test B and Test C
D) It depends on what the criterion is.
E) More than one of the above is correct.

Question 23

Refer to the boxes below, which represent variation in performance, to answer this question: In what type of discussion are these boxes used?

A) Objectivity
B) Shapes
C) Prediction
D) Reliability
E) Squares

Question 24

Refer to the boxes below, which represent variation in performance, to answer this question: Which test battery would you probably NOT use?

A) A
B) B
C) C
D) D
E) It is impossible to determine.

Question 25

Refer to the boxes below, which represent variation in performance, to answer this question: Which test has the smallest SEE?

A) A
B) B
C) C
D) D
E) It is impossible to determine.

Question 26

Estimate the correlation from the following data. Do not calculate the Pearson product-moment correlation coefficient. $\begin{array}{ll}X & Y \\10 & 30 \\2 & 50 \\6 & 40 \\4 & 45 \\8 & 35\end{array}$

A) .00
B) 1.00
C) -.70
D) -1.00
E) It is curvilinear.

Question 27

Describe the general relationship between the coefficient of determination and the SEE.

A) It can be high or it can be low, depending on the situation.
B) They are inversely (negatively) related.
C) They are directly (positively) related.
D) There is no relationship between them.
E) Impossible to determine without knowing the correlation coefficient.

Question 28

Which of the following correlation coefficients provides the most predictive power?

A) +.20
B) -.92
C) -1.09
D) +.84
E) +.48

Question 29

Which of the following probably represents the relationship between VO₂max and time to complete a 1.5-mile run?

A)
B)
C)
D)

Question 30

You want to predict success on your second examination using information from your first examination score. The prediction equation is = 5X + 5, the mean on the first examination is 70, and the standard deviation of the second exam is 20. What is your predicted score on the second exam if you scored 20 on the first exam?

A) 85
B) 95
C) 105
D) You need to know the SEE.
E) None of the above

Question 31

You want to predict success on your second examination using information from your first examination score. The prediction equation is = 5X + 5, the mean on the first examination is 70, and the standard deviation of the second exam is 20. Determine the standard error of estimate for the prediction line if the coefficient of determination between the tests is .64.

A) 8
B) 12
C) 16
D) 24
E) None of the above

Question 32

Mary is predicted to score 140 on an achievement test where the mean was 130 and the standard deviation was 10. How likely is it that her actual score will be at or below 134, if the correlation coefficient between the predictor and the achievement test is .80?

A) 85%
B) 34%
C) 16%
D) 2.5 %
E) More information is needed

Question 33

In general, which type of relationship is best to obtain?

A) An inverse or negative relationship
B) One with a low coefficient of determination
C) One with a low standard error of estimate
D) A direct or positive relationship
E) One with low variability

Question 34

What is the MOST important distinction between simple correlation and multiple correlation?

A) One uses r and the other uses R.
B) The size of the SEE (it is larger with multiple correlation)
C) The amount of variance in Y
D) The number of predictors used for the correlation
E) The number of people used for the correlation

Question 35

Which of the following is/are true if predicting Y from X?

A) The magnitude of the correlation reflects error.
B) The magnitude of the standard error reflects accuracy.
C) he direction of the correlation reflects accuracy.
D) Two of the above are true.
E) All of the above (A, B, and C

Question 36

In the following correlation matrix, skinfolds were taken at four sites in an attempt to estimate percent body fat (%fat). Which of the four skinfolds results in the LARGEST standard error of estimate for estimating %fat? $\begin{array}{|l|c|c|c|c|c|}\hline & \text { \%fat } & \text { Chest } & \text { Abd } & \text { Calf } & \text { Back } \\\hline \text { \%fat } & 1.00 & & & & \\\hline \text { Chest } & .48 & 1.00 & & & \\\hline \text { Abd } & .50 & .62 & 1.00 & & \\\hline \text { Calf } & .58 & .26 & .11 & 1.00 & \\\hline \text { Back } & .62 & .23 & .34 & .42 & 1.00 \\\hline\end{array}$

A) Chest
B) Abd
C) Calf
D) Back
E) It is impossible to determine from what is given.

Question 37

In the following correlation matrix, skinfolds were taken at four sites in an attempt to estimate percent body fat (%fat). Which variables have the LEAST in common? $\begin{array}{|l|c|c|c|c|c|}\hline & \text { \%fat } & \text { Chest } & \text { Abd } & \text { Calf } & \text { Back } \\\hline \text { \%fat } & 1.00 & & & & \\\hline \text { Chest } & .48 & 1.00 & & & \\\hline \text { Abd } & .50 & .62 & 1.00 & & \\\hline \text { Calf } & .58 & .26 & .11 & 1.00 & \\\hline \text { Back } & .62 & .23 & .34 & .42 & 1.00 \\\hline\end{array}$

A) Back and Calf
B) Abd and Calf
C) Chest and Back
D) Chest and Abd
E) Chest and Calf

Question 38

Which of the following represents multiple regression and the largest SEE?

A)
B)
C)
D)

Question 39

Assume the figure below represents the association between self-reported physical activity (Y) and some predictor (X). Which of the following variables illustrates the amount of variance accounted for in this figure? Use the coefficient of determination to find the answer.

A) Skinfolds, which correlates at .50
B) Body fatness, which correlates at .30
C) Age, which correlates at .40
D) 1-mile run time, which correlates at .60
E) Gender, which correlates at .70

Question 40

Most of the examinees who scored below the mean on Test 1 also scored below the mean on Test What kind of correlation would you expect between the two sets of test scores?

A) curvilinear
B) near zero
C) negative
D) positive

Question 41

Using the following data, what is the Pearson product-moment r between X and Y? $\begin{array}{llllll}\text { Subject } & X & Y & X^{2} & Y^{2} & X Y \\1 & 8 & 7 & 64 & 49 & 56 \\2 & 9 & 10 & 81 & 100 & 90 \\3 & 3 & 5 & 9 & 25 & 15 \\4 & 4 & 5 & 16 & 25 & 20 \\5 & \underline{1} & \underline{3} & \underline{1} & \underline{9} & \underline{3} \\\Sigma & 25 & 30 & 171 & 208 & 184\end{array}$

A) .75
B) .78
C) .95
D) .98

Question 42

Using the following data, if each of the five Y scores were multiplied by 3.5, what would be the effect on the calculated r? $\begin{array}{llllll}\text { Subject } & X & Y & X^{2} & Y^{2} & X Y \\1 & 8 & 7 & 64 & 49 & 56 \\2 & 9 & 10 & 81 & 100 & 90 \\3 & 3 & 5 & 9 & 25 & 15 \\4 & 4 & 5 & 16 & 25 & 20 \\5 & \underline{1} & \underline{3} & \underline{1} & \underline{9} & \underline{3} \\\Sigma & 25 & 30 & 171 & 208 & 184\end{array}$

A) It would remain the same.
B) It would increase.
C) It would decrease.
D) It would depend on the shape of the distribution.

Question 43

Which term LEAST belongs with the other three?

A) Correlation
B) Causation
C) Relationship
D) Prediction

Question 44

Which of the following r's has the LEAST predictive power?

A) -.11
B) -.45
C) .23
D) .95

Question 45

If the correlation coefficient between X and Y is .60, what proportion of the variance in Y is NOT predictable from X?

A) .36
B) .40
C) .60
D) .64

Question 46

If the mean and standard deviation for grade point average are 2.0 and .5, respectively, the mean and standard deviation for weight are 100 and 20 respectively, and the r between GPA and weight is .00, what would be the best prediction of GPA for a person weighing 120 pounds?

A) 1.5
B) 2.0
C) 2.5
D) Need to know error of estimate data

Question 47

If variable X correlates at .84 with a criterion variable, what percent of variable X's variance is in common with the criterion?

A) 16%
B) 42%
C) 71%
D) 84%

Question 48

Which of the following is the LEAST likely use of a correlation coefficient?

A) Describing relationships
B) Prediction
C) Assessment of validity and reliability
D) Demonstrating cause and effect

Question 49

Height of a building and amount of sway from wind

A) if r would be definitely positive.
B) if r would be definitely negative.
C) if r would be 0 or nearly 0.

Question 50

Intelligence and strength

A) if r would be definitely positive.
B) if r would be definitely negative.
C) if r would be 0 or nearly 0.

Question 51

Miles driven on a tire and a measure of tire tread

A) if r would be definitely positive.
B) if r would be definitely negative.
C) if r would be 0 or nearly 0.