Deck 14: Correlation and Regression

Question 1

A researcher records the odometer reading 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

Answer 1

B

Question 2

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

Answer 2

C

Question 3

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

Answer 3

A

Question 4

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 5

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 6

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 7

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 violent 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 8

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

A)6/100
B)6/10
C)6/(100/15)
D)6/(10/?0v15)

Question 9

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 10

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

Question 11

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

Question 12

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

A)r = 2/64
B)r = 2/8
C)r = $\surd$ 2/8
D)r = 64/64

Question 13

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 14

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 15

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 16

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 17

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 18

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 19

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

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

Question 20

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 21

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 M_X = 2 and the mean for the Y values is M_Y = 6,what is the Y-intercept value for the regression equation?

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

Question 22

A set of n = 15 pairs of X and Y scores has SS_X = 10,SS_Y = 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 23

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 24

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 25

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 26

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 27

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 28

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

A) $\Sigma$ (X - Y)²
B) $\Sigma$ (Y - Ŷ)
C) $\Sigma$ (Y - Ŷ)²
D)r² $\Sigma$ (Y - Ŷ)²

Question 29

A set of X and Y scores has M_X = 4,SS_X = 10,M_Y = 5,SS_Y = 40,and SP = 20.What is the regression equation for predicting Y from X?

A)
B)
C)
D)

Question 30

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 31

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 32

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 33

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

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

Question 34

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

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

Question 35

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 SS_residual.

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

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 38

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 39

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 40

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 41

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

A)
B)
C)
D)Cannot be determined without additional information

Question 42

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 43

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)df = 1,11
B)df = 1,12
C)df = 2,10
D)df = 2,11

Question 44

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 45

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

Question 46

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 47

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 the relationship with X?

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

Question 48

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 49

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 50

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

Question 51

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 52

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 53

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 54

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

Question 55

The following X and Y scores produce SS_X = 2 and SP = 8.What is regression equation for predicting Y?

A)Y = 0.25X + 4.5 1 2
B)Y = 0.25X - 4.5 2 3
C)Y = 4X + 3
D)Y = 4X - 3

Question 56

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

Question 57

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

A)SS_residual = r²(SS_X)
B)SS_residual = (1 - r²)(SS_X)
C)SS_residual = r²(SS_Y)
D)SS_residual = (1 - r²)(SS_Y)

Question 58

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 59

A researcher obtains SS_X = 20,SS_Y = 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 60

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 61

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 62

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

Question 63

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

Question 64

A sample of n = 25 pairs of scores (X and Y values)produces a correlation of r = -0.40.Are these sample data sufficient to conclude that there is a significant non-zero correlation between X and Y in the population? Use a two-tailed test at the .05 level of significance.

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

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

Question 67

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

Question 68

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 69

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

Question 70

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

Question 71

For linear regression,the value of SS_residual can be computed directly by Σ(Y - ?4Y)².

Question 72

A set of X and Y scores has M_X = 4,M_Y = 10,SS_X = 10,and SP = 5.The regression equation for these scores is Y = 0.5X  8.

Question 73

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 74

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 75

If other factors are held constant,if 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 76

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

Question 77

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 78

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