Deck 14: Linear Regression and Multiple Correlation

Question 1

Which of the following is a disadvantage of multiple correlation compared with Pearson correlation?

A) Interpreting a Pearson correlation is more complicated than interpreting a multiple correlation.
B) Interpreting a multiple correlation is more complicated than interpreting a Pearson correlation.
C) Pearson correlation allows for a better understanding of the relationship between two variables.
D) Pearson correlation allows for a comparison of more than two predictors.

Answer 1

Interpreting a multiple correlation is more complicated than interpreting a Pearson correlation.

Question 2

For a sample of 80 students analyzing 2 predictor variables, what is the degrees of freedom for the numerator of the F-ratio equation?

A) 1
B) 2
C) 78
D) 80

Answer 2

2

Question 3

Correlation differs from regression in that ______.

A) correlation predicts one variable from another
B) correlation compares the means of groups
C) regression predicts one variable from another
D) regression compares the means of groups

Answer 3

regression predicts one variable from another

Question 4

Correlation involves measuring the ______ between variables while regression involves ______.

A) understanding; prediction
B) understanding; relationship
C) prediction; relationship
D) relationship; prediction

Question 5

______ is the use of a relationship between two or more correlated variables to predict values of one variable from values of other variables.

A) Linear regression equation
B) Regression
C) Correlation Matrix
D) Regression coefficient

Question 6

The main purpose of ______ is to ______.

A) correlation; predict scores on a variable
B) regression; determine whether a relationship is linear or nonlinear
C) correlation; test differences between group means
D) regression; predict scores on a variable

Question 7

'Correlation' is to 'regression' as ______.

A) 'samples' are to 'populations'
B) 'linear' is to 'nonlinear'
C) 'significance' is to 'nonsignificance'
D) 'understanding' is to 'prediction'

Question 8

The R is also known as the ______.

A) regression coefficient
B) multiple correlation coefficient
C) correlation coefficient
D) correlation matrix

Question 9

The goal of regression is to ______.

A) produce a straight line that is fitted to a set of data
B) produce a correlation statistics that measures the relationship
C) predict one variable from other variables
D) explain the variance in the criterion

Question 10

For a sample of 100 students analyzing 4 predictor variables, what is the degrees of freedom for the numerator of the F-ratio equation?

A) 2
B) 3
C) 4
D) 100

Question 11

The ______ measures the relationship between two or more predictor variables and a criterion variable.

A) Y
B) X
C) R
D) F

Question 12

______ refers to a statistical procedure in which a straight line is fitted to a set of data to best represent the relationship between two variables.

A) Regression
B) Linear Regression
C) Correlation
D) Multiple correlation

Question 13

'Correlation' is to 'regression' as ______.

A) 'relationship' is to 'prediction'
B) 'significant' is to 'nonsignificant'
C) 'nature' is to 'direction'
D) 'theory' is to 'hypothesis'

Question 14

For a sample of 100 students analyzing 4 predictor variables, what is the degrees of freedom for the denominator of the F-ratio equation?

A) 3
B) 4
C) 95
D) 98

Question 15

Multiple correlation may be defined as ______.

A) the measurement of the relationship between two or more predictor variables and a criterion variable
B) a family of statistical procedures asses the relationship among one predictor variable and a criterion variable
C) a family of statistical procedures assessing the relationship between two or more predictor variables and a criterion variable
D) mathematical equation that predicts a score on a criterion variable from scores on two or more predictor variables

Question 16

The purpose of ______ is to ______.

A) regression; measure the relationship between variables
B) correlation; describe the shape of the distribution
C) correlation; compare groups
D) regression; predict

Question 17

I would calculate a ______ if I wanted to ______.

A) regression equation; test the relationship between variables
B) regression equation; predict one variable from another variable
C) correlation coefficient; compare groups
D) correlation coefficient; test nonlinear relationships

Question 18

The ______ is used to test the significance by transforming R.

A) a
B) b
C) R²
D) F-ratio

Question 19

What measures the combined relationship of all the predictors with the criterion?

A) regression coefficient
B) multiple correlation
C) correlation matrix
D) regression equation

Question 20

______ may be defined as a family of statistical procedures assessing the relationship between two or more predictor variables and a criterion variable.

A) Regression coefficient
B) Linear regression equation
C) Correlation matrix
D) Multiple correlation

Question 21

A researcher studying the relationship between drivers' average speed (MPH) on the highway and number of moving violations they receive develops the following regression equation: Y'= 1.85 + .05(X). In the example, Y'refers to ______.

A) the Y-intercept
B) the slope of the equation
C) a driver's average speed (MPH)
D) a driver's number of moving violations

Question 22

For α = .01 and df = 3, 75, the critical value for the F-ratio would be ______.

A) 3.10
B) 4.94
C) 4.13
D) 2.76

Question 23

A researcher studying the relationship between the number of hours students spend studying and their score on an exam calculates the following regression equation: Y'= 4.07 + .21(X). In this example, Y′ refers to ______.

A) the Y-intercept
B) the slope of the equation
C) predicted exam scores
D) the number of hours spent studying

Question 24

In a sample of 54 students, the combination of household income and high school GPA predicting college GPA had an R = .34, F(3, 50) = 2.34, the researcher would ______.

A) not reject the null hypothesis (p > .05)
B) not reject the null hypothesis (p < .05)
C) reject the null hypothesis (p >.05)
D) reject the null hypothesis (p <.05)

Question 25

For α = .01 and df = 3, 20, the critical value for the F-ratio would be ______.

A) 3.10
B) 4.94
C) 5.85
D) 8.66

Question 26

For α = .05 and df = 4, 90, the critical value for the F-ratio would be ______.

A) 3.64
B) 4.43
C) 5.69
D) 8.66

Question 27

A researcher studying the relationship between people's perceptions of police on their feelings of safety in their neighborhood develops the following regression equation: YF' = 2.14 + .69(X). In this example, Y' refers to ______.

A) the Y-intercept
B) the slope of the equation
C) feelings of safety
D) perceptions of police

Question 28

For α = .05 and df = 3, 20, the critical value for the F-ratio would be ______.

A) 3.10
B) 4.94
C) 5.85
D) 8.66

Question 29

For a sample of 65 students analyzing 3 predictor variables, what is the degrees of freedom for the denominator of the F-ratio equation?

A) 61
B) 63
C) 64
D) 65

Question 30

For a sample of 80 students analyzing 2 predictor variables, what is the degrees of freedom for the denominator of the F-ratio equation?

A) 2
B) 77
C) 78
D) 80

Question 31

In a sample of 60 students, the combination of household income and high school GPA predicting college GPA had an R = .45, F(2, 57) = 7.34, the researcher would ______.

A) not reject the null hypothesis (p > .05)
B) not reject the null hypothesis (p < .05)
C) reject the null hypothesis (p >.05)
D) reject the null hypothesis (p <.05)

Question 32

In a sample of 70 students, the combination of household income and high school GPA predicting college GPA had an R = .54, F(4, 65) = 8.16, the researcher would ______.

A) not reject the null hypothesis (p > .05)
B) not reject the null hypothesis (p < .05)
C) reject the null hypothesis (p >.05)
D) reject the null hypothesis (p <.05)

Question 33

For α = .05 and df = 2, 55, the critical value for the F-ratio would be ______.

A) 3.10
B) 3.23
C) 5.17
D) 19.47

Question 34

A researcher studying the relationship between drivers' average speed (MPH) on the highway and number of moving violations they receive develops the following regression equation: Y'= 1.85 + .05(X). In this example, 1.85 refers to ______.

A) the Y-intercept
B) the slope of the equation
C) a driver's average speed (MPH)
D) a driver's number of moving violations

Question 35

In a sample of 60 students, the combination of household income and high school GPA predicting college GPA had an R = .45, F(2, 57) = 7.34, the researcher would ______.

A) not reject the null hypothesis (p > .05)
B) not reject the null hypothesis (p < .05)
C) reject the null hypothesis (p >.05)
D) reject the null hypothesis (p <.05)

Question 36

A researcher studying the relationship between the number of hours students spend studying and their score on an exam calculates the following regression equation: Y' = 4.07 + .21(X). In this example, .21 refers to ______.

A) the Y-intercept
B) the slope of the equation
C) exam scores
D) the number of hours spent studying

Question 37

For a sample of 65 students analyzing 3 predictor variables, what is the degrees of freedom for the numerator of the F-ratio equation?

A) 1
B) 2
C) 3
D) 65

Question 38

A researcher studying the relationship between people's perceptions of police on their feelings of safety in their neighborhood develops the following regression equation: Y' = 2.14 + .69(X). In this example, X refers to ______.

A) the Y-intercept
B) the slope of the equation
C) feelings of safety
D) perceptions of police

Question 39

A researcher studying the relationship between drivers' average speed (MPH) on the highway and number of accidents they have been involved in develops the following regression equation: Y'= 1.75 + .03(X). In this example, X refers to ______.

A) the Y-intercept
B) the slope of the equation
C) a driver's average speed (MPH)
D) a driver's number of accidents

Question 40

In a sample of 35 students, the combination of household income and high school GPA predicting college GPA had an R = .45, F(2, 32) = 4.25, the researcher would ______.

A) not reject the null hypothesis (p > .05)
B) not reject the null hypothesis (p < .05)
C) reject the null hypothesis (p >.05)
D) reject the null hypothesis (p <.05)

Question 41

If you were to develop a linear regression equation that predicts the number of arrests from age, what would be the Y-intercept (a) of the regression equation? Pearson r = .25

A) 0.014
B) 0.51
C) 0.59
D) 1.49

Question 42

A researcher studying the relationship between drivers' average speed (MPH) on the highway and number of accidents they have been involved in develops the following regression equation: Y' = 1.75 + .03(X). In this example, if a driver's average driving speed is 75 MPH, you would predict he or she would get into ______ accidents

A) .03
B) 1.75
C) 4
D) 75

Question 43

If you were to develop a linear regression equation that predicts violent behaviors from education and age, what would be the Y-intercept (a) of the regression equation?

A) 13.20
B) -8.06
C) -1.49
D) 3.65

Question 44

The first step in calculating the linear regression equation is to ______.

A) calculate the Y-intercept
B) calculate the X-intercept
C) calculate the slope
D) state the null hypothesis

Question 45

For data that produced a slope of .36 and an intercept of 5.23, which is the appropriate way to report the linear regression equation?

A) 5.23 = a + .36 (X)
B) Y' = 36 + 5.23 (X)
C) Y' = 5.23 + .36 (X)
D) Y' = 5.23 + b (.36)

Question 46

If you were to develop a linear regression equation that predicts the number of arrests from years of education, what would be the Y-intercept (a) of the regression equation? Pearson r = .36

A) 1.11
B) 1.13
C) 0.10
D) 0.28

Question 47

For data that yielded an intercept of 3.66 and a slope of .15, what would be the appropriate linear regression equation?

A) 3.66 = a + .15 (X)
B) 3.66 = a + b (.15)
C) Y' = 3.66 + b (.15)
D) Y' = 3.66 + .15 (X)

Question 48

If there is no relationship between two variables, the linear regression equation looks like a ______ line.

A) skewed
B) curved
C) horizontal
D) normal

Question 49

If you were to develop a linear regression equation that predicts the number of crimes from age, what would be the slope (b) of the regression equation? Pearson r = .30

A) .06
B) .21
C) .30
D) 1.46

Question 50

If you were to develop a linear regression equation that predicts violent behaviors from number of times in prison and age, what would be the Y-intercept (a) of the regression equation?

A) 13.20
B) 11.13
C) 4.56
D) 3.65

Question 51

If you were to develop a linear regression equation that predicts the number of victimizations from age, what would be the Y-intercept (a) of the regression equation? Pearson r = .41

A) -166.86
B) -3.39
C) 3.27
D) -.29

Question 52

Which of these scatterplots is most likely to result in the regression equation Y' = 2.25 - .45(X)? Figure A Figure B Figure C Figure D

A) Figure A
B) Figure B
C) Figure C
D) Figure D

Question 53

For data that yielded an intercept of 7.54 and a slope of .64, what would be the appropriate linear regression equation?

A) 7.54 = a + .64 (X)
B) 7.54 = a + b (.64)
C) Y'= 7.54 + b (.64)
D) Y' = 7.54 + .64 (X)

Question 54

If you were to develop a linear regression equation that predicts the number of victimizations from education, what would be the Y-intercept (a) of the regression equation? Pearson r = .29

A) 0.09
B) 0.32
C) 1.13
D) 3.08

Question 55

A researcher studying the relationship between people's perceptions of police on their feelings of safety in their neighborhood develops the following regression equation: Y' = 2.14 + .69(X). In this example, .69 refers to ______.

A) the Y-intercept
B) the slope of the equation
C) feelings of safety
D) perceptions of police

Question 56

In linear regression, the Y-intercept a is the predicted value for the Y variable when X is equal to ______.

A) .01
B) 0
C) 1.0
D) -1.0

Question 57

If you were to develop a linear regression equation that predicts the number of crimes from age, what would be the Y-intercept (a) of the regression equation? Pearson r = .30

A) -166.86
B) -26.90
C) 3.27
D) 31.79

Question 58

A researcher studying the effect of gender on feelings of safety at night develops the following regression equation: Y' = 1.12 + .98(X). In this example, Y' refers to ______, .98 refers to ______, and X refers to ______.

A) feelings of safety; the slope of the equation; gender
B) the slope of the equation; feelings of safety; gender
C) gender; the slope of the equation; feelings of safety
D) the intercept; the slope of the equation; gender

Question 59

If you were to develop a linear regression equation that predicts violent behaviors from education and number of times in prison, what would be the Y-intercept (a) of the regression equation?

A) -1.49
B) 0.58
C) 4.56
D) 3.65

Question 60

If there is zero correlation between two variables, the linear regression equation based on this correlation is a ______ line.

A) vertical
B) horizontal
C) curved
D) dotted

Question 61

When there is no relationship between variables, ______.

A) the scatterplot is inaccurate
B) an accurate prediction of the mean of the other variable can be made
C) a calculation error has been made
D) no accurate prediction can be made

Question 62

The R measures the relationship between two or more predictor variables and a criterion variable.

Question 63

Multiple correlation is defined as the mathematical equation that predicts a score on a criterion variable from scores on two or more predictor variables.

Question 64

The linear regression equation represents ______.

A) the value of X
B) the value of Y
C) the "best fit" relationship between two variables
D) a horizontal relationship

Question 65

The R is also known as the regression coefficient

Question 66

A correlation matrix is ______.

A) a table of Pearson correlations between variables
B) a scatterplot display
C) a representation of the linear regression equation
D) the point of the Y-intercept

Question 67

Including multiple predictors in one analysis ______.

A) guarantees significant results
B) is less accurate than using only one predictor
C) offers no real research advantage
D) should increase the amount of explained variance in the criterion

Question 68

Correlation involves measuring the relationship between variables.

Question 69

Multiple correlation is defined as a family of statistical procedures assessing the relationship between two or more predictor variables and a criterion variable.

Question 70

Developing a linear regression equation requires calculating the slope (b) and ______.

A) the X intercept
B) the value of t
C) the value of m
D) the Y-intercept (a)

Question 71

Correlation involves the prediction of a criterion variable while regression involves measuring the relationship between variables.

Question 72

Multiple correlation provides researchers the ability to ______.

A) test a variety of effects
B) accurately support the alternative hypothesis
C) provide assurance of significant results
D) easily calculate results

Question 73

When a relationship is found between variables, an opportunity exists to ______.

A) predict one variable from another
B) reject the null hypothesis
C) reject the alternative hypothesis
D) prove the validity of the research

Question 74

The multiple regression equation may be reported once the ______.

A) regression coefficients have been calculated
B) Y-intercept has been calculated
C) slope has been determined
D) regression coefficient and the Y-intercept have been calculated

Question 75

Regression involves the prediction of a criterion variable.

Question 76

The F-ratio is used to test the significance by transforming R.

Question 77

In the regression equation: Y′ = 3.66 + .15(X). Y′ refers to the Y-intercept.

Question 78

Multiple correlation measures the combined relationship of all the predictors with the criterion.

Question 79

A multiple correlation R is significant when it is statically ______.

A) equal to 1.0
B) different from .00
C) equal to .01
D) different from 1.0

Question 80

The value for the slope of the regression equation is ______.

A) always a positive number
B) always a negative number
C) either positive or negative
D) a squared result