Deck 14: Correlation and Regression.

Question 1

A researcher measures IQ and weight for a group of college students.What kind of correlation is likely to be obtained for these two variables?

A)A positive correlation
B)A negative correlation
C)A correlation near zero
D)A correlation near one

Answer 1

A correlation near zero

Question 2

A set of n = 5 pairs of X and Y values has SSₓ = 16,SSʏ = 4 and SP = 2.For these data,what is the Pearson correlation?

A)r = 2/64
B)r = 2/8
C)r = √2/8
D)r = 64/64

Answer 2

r = 2/8

Question 3

What is indicated by a positive value for a correlation?

A)Increases in X tend to be accompanied by increases in Y
B)Increases in X tend to be accompanied by decreases in Y
C)A much stronger relationship than if the correlation were negative
D)A much weaker relationship than if the correlation were negative

Answer 3

Increases in X tend to be accompanied by increases in Y

Question 4

For a two-tailed hypothesis test evaluating a Pearson correlation,what is stated by the null hypothesis?

A)There is a non-zero correlation for the general population.
B)The population correlation is zero.
C)There is a non-zero correlation for the sample.
D)The sample correlation is zero.

Question 5

Which of the following Pearson correlations shows the greatest strength or consistency of relationship?

A)-0.90
B)+0.74
C)+0.85
D)-0.33

Question 6

What would the scatter plot show for data that produce a Pearson correlation of r = +0.88?

A)Points clustered close to a line that slopes up to the right
B)Points clustered close to a line that slopes down to the right
C)Points widely scattered around a line that slopes up to the right
D)Points widely scattered around a line that slopes down to the right

Question 7

A set of n = 10 pairs of scores has ΣX = 20,ΣY = 30,and ΣXY = 74.What is the value of SP for these data?

A)74
B)24
C)14
D)-14

Question 8

Which of the following best describes the Pearson correlation for these data? $$\begin{array} { l l } \mathrm { X } & \mathrm { Y } \\\hline 2 & 5 \\5 & 1 \\3 & 4 \\4 & 2\end{array}$$

A)Positive
B)Negative
C)Zero
D)Cannot be determined

Question 9

What is indicated by a Pearson correlation of r = +1.00 between X and Y?

A)Each time X increases, there is a perfectly predictable increase in Y
B)Every change in X causes a change in Y
C)Every increase in X causes an increase in Y
D)All of the other 3 choices occur with a correlation of +1.00.

Question 10

The scatter plot for a set of X and Y values shows the data points clustered in a nearly perfect circle.For these data,what is the most likely value for the Pearson correlation?

A)A positive correlation near 0
B)A negative correlation near 0
C)Either positive or negative near 0
D)A value near +1.00 or -100

Question 11

A set of n = 15 pairs of scores (X and Y values)has SSₓ = 4,SSʏ = 25,and SP = 6.What is the Pearson correlation for these data?

A)6/100
B)6/10
C)6/(100/15)
D)6/(100-15))

Question 12

A set of n = 5 pairs of X and Y scores has ΣX = 15,ΣY = 5,and ΣXY = 10.For these data,what is the value of SP?

A)-5
B)5
C)10
D)25

Question 13

A researcher records the age and price for a group of used Hondas.What kind of correlation is likely to be obtained for these two variables?

A)A positive correlation
B)A negative correlation
C)A correlation near zero
D)A correlation near one

Question 14

The results from a research study indicate that adolescents who watch more violent content on television also tend to engage in more violent behavior than their peers.The correlation between amount of TV violence content and amount of violent behavior is an example of _______.

A)a positive correlation
B)a negative correlation
C)a correlation near zero
D)a correlation near one

Question 15

What is the value of SP for the following set of data? $$\begin{array} { l l } \mathrm { X } & \mathrm { Y } \\\hline 1 & 4 \\2 & 4 \\9 & 1\end{array}$$

A)5
B)-5
C)15
D)-15

Question 16

What is the value of SP for the following set of data? $$\begin{array} { l l } \mathrm { X } & \mathrm { Y } \\\hline 4 & 3 \\1 & 2 \\1 & 5 \\2 & 6\end{array}$$

A)-1
B)-5 4
C)5 1
D)None of the other 3 choices is correct.

Question 17

Suppose the correlation between height and weight for adults is +0.40.What proportion (or percent)of the variability in weight can be explained by the relationship with height?

A)40%
B)60%
C)16%
D)84%

Question 18

A researcher measures driving distance from college and weekly cost of gas for a group of commuting college students.What kind of correlation is likely to be obtained for these two variables?

A)A positive correlation
B)A negative correlation
C)A correlation near zero
D)A correlation near one

Question 19

For which of the following Pearson correlations would the data points be clustered most closely around a straight line?

A)-0.10
B)+0.40
C)-0.70
D)There is no relationship between the correlation and how close the points are to a straight line.

Question 20

A set of n = 15 pairs of scores (X and Y values)produces a correlation of r = 0.40.If each of the X values is multiplied by 2 and the correlation is computed for the new scores,what value will be obtained for the new correlation?

A)r = 0.20
B)r = 0.40
C)r = 0.80
D)Cannot be determined without knowing all the X and Y scores

Question 21

A set of n = 15 pairs of X and Y scores has SSₓ = 10,SSʏ = 40,and SP = 30.What is the slope for the regression equation for predicting Y from X?

A)10/30
B)10/40
C)40/10
D)30/10

Question 22

For the regression equation Ŷ = -2X + 6,what can be determined about the correlation between X and Y?

A)The correlation definitely will be positive.
B)The correlation definitely will be negative.
C)The correlation will be relatively large and positive
D)The correlation will be relatively large and negative.

Question 23

As the sample size gets larger,what happens to the size of the correlation that is needed for significance?

A)It also gets larger.
B)It gets smaller.
C)It stays constant.
D)There is no consistent relationship between sample size and the critical value for a significant correlation.

Question 24

The regression equation is determined by finding the minimum value for which of the following?

A)?(X - Y)²
B)?(Y - ?)
C)?(Y - ?)²
D)r²?(Y - ?)²

Question 25

A set of X and Y scores has MX = 4,SSₓ = 10,MY = 5,SSʏ = 40,and SP = 20.What is the regression equation for predicting Y from X?

A)Ŷ = 0.25X + 4
B)Ŷ = 4X - 9
C)Ŷ = 0.5X + 3
D)Ŷ = 2X - 3

Question 26

A researcher obtains a Pearson correlation of r = 0.60 for a sample of n = 6 pairs of X and Y scores.If the researcher tests the significance of the correlation,what value will be obtained for the t statistic?

A)0.6/0.16 = 3.75
B)0.6/0.4 = 1.50
C)0/6/0.8 = 0.77
D)0.6/1.0 = 0.6

Question 27

Which correlation should be used to measure the relationship between gender and grade point average for a group of college students?

A)Pearson correlation
B)Spearman correlation
C)Point-biserial correlation
D)Phi-coefficient

Question 28

If the following seven scores are ranked from smallest (#1)to largest,what rank should be assigned to a score of X = 6? Scores: 1,1,3,6,6,6,9

A)3
B)4
C)5
D)6

Question 29

For the linear equation Y = 2X - 3,which of the following points will not be on the line?

A)0, -3
B)2, 1
C)3, 0
D)4, 5

Question 30

For the regression equation Y = X - 2,if the mean for Y is MY = 6,what is the mean for X?

A)4
B)6
C)8
D)10

Question 31

The Pearson and the Spearman correlations are both computed for the same set of data.If the Spearman correlation is r_S = +1.00,what can you conclude about the Pearson correlation?

A)It will be positive.
B)It will have a value of 1.00.
C)It will be positive and have a value of 1.00.
D)There is no predictable relationship between the Pearson and the Spearman correlations.

Question 32

The effect size for the data from an independent-measures t test can be measured by r²,which is the percentage of variance accounted for.Which of the following also produces the value for r²?

A)Squaring the Spearman correlation for the same data
B)Squaring the point-biserial correlation for the same data
C)Squaring the Pearson correlation for the same data
D)None of the other options will produce r².

Question 33

Under what circumstances is the phi-coefficient used?

A)When one variable consists of ranks and the other is regular, numerical scores
B)When both variables consists of ranks
C)When both X and Y are dichotomous variables
D)When one variable is dichotomous and the other is regular, numerical scores

Question 34

If the following nine scores are ranked from smallest (#1)to largest,what rank should be assigned to a score of X = 1? Scores: 1,1,1,1,3,6,6,6,9

A)1
B)2
C)2.5
D)4

Question 35

For the regression equation Y = 2X - 3,if the mean for X is MX = 5,what is the mean for Y?

A)2
B)4
C)5
D)7

Question 36

For the linear equation Y = 2X + 4,if X increases by 1 point,how much will Y increase?

A)1 points
B)2 points
C)3 points
D)4 points

Question 37

What correlation is obtained when the Pearson correlation is computed for data that have been converted to ranks?

A)The Spearman correlation
B)The point-biserial correlation
C)The phi coefficient
D)It is still called a Pearson correlation.

Question 38

For a group of graduating college seniors,a researcher records each student's rank in his/her high school graduating class and the student's rank in the college graduating class.Which correlation should be used to measure the relationship between these two variables?

A)Pearson correlation
B)Spearman correlation
C)Point-biserial correlation
D)Phi-coefficient

Question 39

The Pearson correlation is calculated for a sample of n = 20 individuals.If a hypothesis test is used to determine whether the correlation is significant,what df value would be used for the t statistic?

A)18
B)19
C)20
D)21

Question 40

A set of X and Y scores has a regression equation with a slope of b = 4.If the mean for the X values is MX = 2 and the mean for the Y values is MY = 6,what is the Y-intercept value for the regression equation?

A)-2
B)-22
C)4
D)-4

Question 41

A researcher obtains SSₓ = 20,SSʏ = 5,and SP = 7 for a set of n = 25 pairs of scores.The Pearson correlation for these scores is r = 7/10 = 0.70.

Question 42

If you measured hearing acuity and age for a group of people who are 50 to 90 years old,you should obtain a positive correlation between the two variables.

Question 43

Suppose that there is a correlation of r = 0.41 between the amount of time that each student reports studying for an exam and the student's grade on the exam.This correlation would mean that there is a tendency for people who study more to get better grades.

Question 44

One or two extreme data points can have a dramatic effect on the size of a correlation.

Question 45

If the value of the Pearson correlation is r = +1.00 or -1.00,then all data points in a scatter plot fit perfectly on a straight line.

Question 46

The following X and Y scores produce SS? = 2 and SP = 8.What is regression equation for predicting Y? $$\begin{array} { l l } \mathrm { X } & \mathrm { Y } \\\hline 1 & 2 \\2 & 3 \\3 & 10\end{array}$$

A)Y = 0.25X + 4.5
B)Y = 0.25X - 4.5
C)Y = 4X + 3
D)Y = 4X - 3

Question 47

The distance between the Y value in the data and the predicted Y value from the regression equation is known as the residual.What is the value for the sum of the squared residuals?

A) $S S _ { \text {residual } }$ = r²(SS?)
B) $S S _ { \text {residual } }$ = (1 - r²)(SS?)
C) $S S _ { \text {residual } }$ = r²(SS?)
D) $S S _ { \text {residual } }$ = (1 - r²)(SS?)

Question 48

A set of n = 25 pairs of scores (X and Y values)has a Pearson correlation of r = 0.80.How much of the variance for the Y scores is predicted by its relationship with X?

A)0.36 or 36%
B)0.20 or 20%
C)0.80 or 80%
D)0.64 or 64%

Question 49

A negative correlation means that decreases in the X variable tend to be accompanied by decreases in the Y variable.

Question 50

The value obtained for the sum of products,SP,determines the sign (+/-)for the Pearson correlation.

Question 51

A Pearson correlation of r = -0.90 indicates that the data points are clustered close to a line that slopes down to the right.

Question 52

A linear regression equation has b = 3 and a = - 6.What is the predicted value of Y for X = 4?

A)Ŷ = 6
B)Ŷ = -21
C)Ŷ = -2
D)Cannot be determined without additional information

Question 53

For linear regression calculated for a sample of n = 20 pairs of X and Y values,what is the value for degrees of freedom for the predicted portion of the Y-score variance,MS regression?

A)1
B)2
C)19
D)18

Question 54

A set of X and Y scores has a Pearson correlation of r = -0.60.For these data,60% of the variability in the Y scores can be predicted from the relationship with X.

Question 55

Assuming that SS_y is constant,which of the following correlations would have the largest SS_residual?

A)r = -0.10
B)r = +0.40
C)r = -0.70
D)There is no relationship between the correlation and $S S _ { \text {residual } }$ .

Question 56

A researcher finds a significant correlation between the amount of time spent watching television and blood pressure for a sample of 40-year-old men.This means that watching more television causes high blood pressure.

Question 57

If there is a positive correlation between X and Y,then the regression equation Y = bX + a will have _____.

A)b > 0
B)b < 0
C)a > 0
D)a < 0

Question 58

A linear regression equation is computed for a sample of n = 13 pairs of X and Y scores.For the analysis of regression testing the significance of the equation,what are the df values for the F-ratio?

A)1, 11
B)1, 12
C)2, 10
D)2, 11

Question 59

For the regression equation,Ŷ = -2X + 6,if the X value is above the mean (positive deviation),what can be determined about the predicted Y value?

A)The predicted Y value will be above the mean for the Y scores.
B)The predicted Y value will be below the mean for the Y scores.
C)The predicted Y value will be equal to the mean for the Y scores.
D)It is impossible to determine where the predicted Y value will be.

Question 60

An analysis of regression is used to test the significance of a linear regression equation based on a sample of n = 20 individuals.What are the df values for the F-ratio?

A)1, 18
B)1, 19
C)2, 18
D)2, 19

Question 61

The line defined by the equation Y = -3X + 6 slopes up to the right.

Question 62

The F-ratio evaluating the significance of a linear regression equation based on n = 10 pairs of X and Y scores has df = 1,9.

Question 63

For a regression equation with a slope of b = 3,if MX = 3 and MY = 10,then the Y-intercept for the equation is 1.

Question 64

If the Spearman correlation for a set of scores is equal to +1.00,then the Pearson correlation for the same scores would also be equal to +1.00.

Question 65

If people are classified by age (over 30/under 30)and by political affiliation (Democrat/Republican),then the point-biserial correlation would be the proper technique to measure the relationship between the two variables.

Question 66

If the Pearson correlation between X and Y is r = 0.60,then the regression equation predicts 36% of the variance in the Y scores.

Question 67

In a test for significance of a Pearson correlation for a sample of n = 30 individuals,you determine the critical value by using df = 29.

Question 68

The phi-coefficient is used to measure relationships for data that would also be appropriate for an independent-measures t test.

Question 69

A set of X and Y scores has SSₓ = 10,SSʏ = 36,and SP = 20.The regression equation for these scores will have a slope constant of 2.

Question 70

A set of X and Y scores has MX = 4,MY = 10,SSₓ = 10,and SP = 5.The regression equation for these scores is Y = 0.5X + 8.

Question 71

It is possible for none of the actual (observed)data points to be located on the regression line described by the regression equation.

Question 72

The sign of the correlation (+/-)is generally meaningless for the point-biserial correlation and the phi-coefficient.

Question 73

The phi-coefficient is the correct correlation to use when both X and Y are dichotomous variables.

Question 74

For linear regression,the value of SSᵣₑsᵢdᵤₐl can be computed directly by Σ(Y -Ŷ)².

Question 75

For a regression equation with a positive slope,if the X value is above the mean for the X scores,then the predicted Y value will be above the mean for the Y scores.

Question 76

If other factors are held constant and the Pearson correlation between X and Y is r = 0.80,then the regression equation will produce more accurate predictions than would be obtained if r = 0.60.

Question 77

For a two-tailed hypothesis test evaluating the significance of a correlation,the null hypothesis states that the sample correlation is zero.

Question 78

If the Pearson correlation for a set of scores is equal to +1.00,then the Spearman correlation for the same scores would also be equal to +1.00.

Question 79

Assuming that other factors are constant,a correlation of r = -0.95 will result in more accurate predictions than a correlation of r = +0.70.

Question 80

The line produced by the equation Y = 4X - 5 crosses the vertical axis at Y = 5.