# Quiz 14: Multiple Regression Analysis

Statistics

Q 1Q 1

Multiple regression analysis is used when one independent variable is used to predict values of two or more dependent variables.

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True False

False

Q 2Q 2

If the hypothesis H

_{0}: β_{1}= 0 is rejected,then the sample regression coefficient b_{1}indicates the change in the predicted value for a unit change in X_{1}when all other X_{i}variables are held constant.Free

True False

True

Q 3Q 3

The coefficient of multiple determination,R

^{2},reports the proportion of the variation in Y that is not explained by the variation in the set of independent variables.Free

True False

False

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True False

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True False

Q 6Q 6

In multiple regression analysis,an F-statistic is used to test the global hypothesis,H

_{0}: All β_{i}= 0Free

True False

Q 7Q 7

In a multiple regression analysis,if the regression coefficient of a dummy variable is significant and has a sample value of 100,then the dummy variable's effect on the dependent variable is an increase of 100.

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True False

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True False

Q 9Q 9

The variance inflation factor (VIF)is used to select or remove independent variables to reduce the effects of multicollinearity in a multiple regression equation.

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True False

Q 10Q 10

In multiple regression analysis,a residual is the difference between the value of an independent variable and its corresponding dependent-variable value.

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True False

Q 11Q 11

For a global test of a multiple regression equation,the F-distribution is defined by the regression and residual degrees of freedom.

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True False

Q 12Q 12

Stepwise regression analysis is a method that assists in selecting the most significant variables for a multiple regression equation.

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True False

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True False

Q 14Q 14

Interaction occurs when the relationship between an independent variable and a dependent variable is affected by another independent variable.

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True False

Q 15Q 15

In a multiple regression equation with three independent variables,X

_{1},X_{2},and X_{3},the interaction term is expressed as (Y)(X_{1}).Free

True False

Q 16Q 16

To evaluate the assumption of linearity,a multiple regression analysis should include ________.
A)a calculation of variance inflation factors
B)hypothesis tests of individual regression coefficients
C)scatter diagrams of the dependent variable plotted as a function of each independent variable
D)an ANOVA table

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Multiple Choice

Q 17Q 17

In multiple regression analysis,residual analysis is used to test the requirement that ________.
A)the variation in the residuals is the same for all predicted values of Y
B)the independent variables are the direct cause of the dependent variable
C)the number of independent variables included in the analysis is correct
D)the prediction error is minimized

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Multiple Choice

Q 18Q 18

A valid multiple regression analysis assumes or requires that ________.
A)the dependent variable is measured using an ordinal,interval,or ratio scale
B)the residuals follow an F-distribution
C)the independent variables and the dependent variable have a linear relationship
D)the observations are auto correlated

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Multiple Choice

Q 19Q 19

In multiple regression analysis,how is the degree of association between a set of independent variables and a dependent variable measured?
A)Confidence intervals
B)Autocorrelation
C)Coefficient of multiple determination
D)Standard error of estimate

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Multiple Choice

Q 20Q 20

In an ANOVA table,for a multiple regression analysis,the variation of the dependent variable explained by the variation of the independent variables is represented by ________.
A)the regression sum of squares
B)the total sum of squares
C)the residual mean square
D)the p-value

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Multiple Choice

Q 21Q 21

If the coefficient of multiple determination is 0.81,what percent of variation is not explained?
A)19%
B)90%
C)66%
D)81%

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Multiple Choice

Q 22Q 22

In multiple regression analysis,testing the global null hypothesis that all regression coefficients are zero is based on ________.
A)a z-statistic
B)a t-statistic
C)an F-statistic
D)a binomial distribution

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Multiple Choice

Q 23Q 23

When expressed as a percentage,what is the range of values for multiple R

^{2}? A)−100% to +100% inclusive B)−100% to 0% inclusive C)0% to +100% inclusive D)Unlimited rangeFree

Multiple Choice

Q 24Q 24

The adjusted R

^{2}accounts for the number of independent variables by ________. A)adding one to the R^{2}B)using the degrees of freedom C)multiplying by the multiple standard error of the estimate D)using a subscript for R^{2}Free

Multiple Choice

Q 25Q 25

When does multicollinearity occur in a multiple regression analysis?
A)When the dependent variables are highly correlated
B)When the regression coefficients are correlated
C)When the independent variables are highly correlated
D)When the independent variables have no correlation

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Multiple Choice

Q 26Q 26

In multiple regression analysis,when the independent variables are highly correlated,this situation is called ________.
A)autocorrelation
B)multicollinearity
C)homoscedasticity
D)curvilinearity

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Multiple Choice

Q 27Q 27

In the general multiple regression equation,which of the following variables represents the Y-intercept?
A)b

_{1}B)X_{1}C) D)aFree

Multiple Choice

Q 28Q 28

If there are four independent variables in a multiple regression equation,there are also four ________.
A)Y-intercepts
B)regression coefficients
C)dependent variables
D)constant terms

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Multiple Choice

Q 29Q 29

If a data set of 10 observations is used in a multiple regression analysis with 10 independent variables,then ________.
A)R

^{2}will be equal to 1.0 B)the multiple standard error of the estimate will be 1.0 C)the independent variables will be correlated D)the regression coefficients will all equal 1.0Free

Multiple Choice

Q 30Q 30

What does the multiple standard error of estimate measure?
A)The change in Ŷ for a change in X

_{1}B)The variability of the residuals C)The regression mean square error in the ANOVA table D)The amount of explained variationFree

Multiple Choice

Q 31Q 31

In multiple regression analysis,before testing the significance of the individual regression coefficients,________.
A)the intercept must equal 0
B)the multiple standard error of the estimate must be less than the error mean square
C)the null hypothesis that all regression coefficients equal zero must not be rejected
D)the null hypothesis that all regression coefficients equal zero must be rejected

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Multiple Choice

Q 32Q 32

The variance inflation factor can be used to reduce multicollinearity by ________.
A)eliminating variables for a multiple regression model
B)decreasing homoscedasticity
C)evaluating the distribution of residuals
D)testing the null hypothesis that all regression coefficients equal zero

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Multiple Choice

Q 33Q 33

If a multiple regression analysis is based on 10 independent variables collected from a sample of 125 observations,what is the value of the denominator in the calculation of the multiple standard error of estimate?
A)125
B)10
C)114
D)115

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Multiple Choice

Q 34Q 34

If the correlation between the two independent variables of a regression analysis is 0.11,and each independent variable is highly correlated to the dependent variable,what does this indicate?
A)Multicollinearity between these two independent variables.
B)A negative relationship is not possible.
C)Only one of the two independent variables will explain a high percent of the variation.
D)An effective regression equation.

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Multiple Choice

Q 35Q 35

If the correlation between the two independent variables of a regression analysis is 0.11 and each independent variable is highly correlated to the dependent variable,what does this indicate?
A)Only one of the independent variables should be used in the regression equation.
B)The independent variables are strongly related.
C)Two separate regression equations are required.
D)Both independent variables should be used to predict the dependent variable.

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Multiple Choice

Q 36Q 36

What does the correlation matrix for a multiple regression analysis contain?
A)Multiple correlation coefficients
B)Simple correlation coefficients
C)Multiple coefficients of determination
D)Multiple standard errors of estimate

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Multiple Choice

Q 37Q 37

What can we conclude if the global test of regression does not reject the null hypothesis?
A)A strong relationship exists among the variables.
B)No relationship exists between the dependent variable and any of the independent variables.
C)The independent variables are good predictors.
D)Good forecasts are possible.

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Multiple Choice

Q 38Q 38

What can we conclude if the global test of regression rejects the null hypothesis?
A)Strong correlations exist among the variables.
B)No relationship exists between the dependent variable and any of the independent variables.
C)At least one of the regression coefficients is not equal to zero.
D)Good predictions are not possible.

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Multiple Choice

Q 39Q 39

The degrees of freedom associated with the regression sum of squares equals ________.
A)the number of independent variables
B)1
C)the F-ratio
D)(n − 2)

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Multiple Choice

Q 40Q 40

Which of the following is a characteristic of the F-distribution?
A)Normally distributed
B)Positively skewed
C)Negatively skewed
D)Equal to the t-distribution

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Multiple Choice

Q 41Q 41

In a regression analysis,three independent variables are used in the equation based on a sample of 40 observations. In the ANOVA table for a multiple regression analysis,what are the degrees of freedom associated with the F-statistic?
A)3 and 39
B)4 and 40
C)3 and 36
D)2 and 39

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Multiple Choice

Q 42Q 42

Which statistic is used to test hypotheses about individual regression coefficients?
A)t-statistic
B)z-statistic
C)

^{Χ}^{2 }(chi-square statistic) D)FFree

Multiple Choice

Q 43Q 43

Which statistic is used to test a global hypothesis about a multiple regression equation?
A)t-statistic
B)z-statistic
C)

^{Χ}^{2}(chi-square statistic) D)FFree

Multiple Choice

Q 44Q 44

The coefficient of determination measures the proportion of ________.
A)explained variation relative to total variation
B)variation due to the relationship among variables
C)error variation relative to total variation
D)variation due to regression

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Multiple Choice

Q 45Q 45

What happens as the scatter of data values about the regression plane increases?
A)The standard error of estimate increases.
B)R

^{2}increases. C)(1 − R^{2})decreases. D)The error sum of squares decreases.Free

Multiple Choice

Q 46Q 46

All other things being held constant,what is the change in the dependent variable for a unit change in X

_{1}for the multiple regression equation: Ŷ = 5.2 + 6.3X_{1}− 7.1 X_{2}? A)−7.1 B)+6.3 C)+5.2 D)+4.4Free

Multiple Choice

Q 47Q 47

The best example of a null hypothesis for a global test of a multiple regression model is ________.
A)H

_{0}: β_{1}= β_{2}= β_{3}= β_{4}= 0 B)H_{0}: µ_{1}= µ_{2}= µ_{3}= µ_{4}= 0 C)H_{0}: β_{1}= 0 D)if F is greater than 20.00,then rejectFree

Multiple Choice

Q 48Q 48

The best example of an alternate hypothesis for a global test of a multiple regression model is ________.
A)H

_{1}: β_{1}= β_{2}= β_{3}= β_{4}= 0 B)H_{1}: β_{1}≠ β_{2}≠ β_{3}≠ β_{4}≠ 0 C)H_{1}: Not all the β_{i}'s are equal to 0. D)if F is less than 20.00,then fail to reject.Free

Multiple Choice

Q 49Q 49

The best example of a null hypothesis for testing an individual regression coefficient is ________.
A)H

_{0}: β_{1}= β_{2}= β_{3}= β_{4}= 0 B)H_{0}: µ_{1}= µ_{2}= µ_{3}= µ_{4}= 0 C)H_{0}: β_{1}= 0 D)H_{0}: β_{1}≠ 0Free

Multiple Choice

Q 50Q 50

In multiple regression analysis,residuals (Y − )are used to ________.
A)provide a global test of a multiple regression model
B)evaluate multicollinearity
C)evaluate homoscedasticity
D)compare two regression coefficients

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Multiple Choice

Q 51Q 51

In multiple regression analysis,residuals (Y − )are used to ________.
A)provide a global test of a multiple regression model
B)evaluate the assumption of linearity
C)calculate the variance inflation factor
D)compare two regression coefficients

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Multiple Choice

Q 52Q 52

In multiple regression analysis,residuals (Y − )should be ________.
A)qualitative variables
B)significantly different from zero
C)correlated
D)normally distributed with a mean of zero

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Multiple Choice

Q 53Q 53

In multiple regression analysis,a dummy variable is ________.
A)an additional quantitative variable
B)a nominal variable with three or more values
C)a nominal variable with only two values
D)a new regression coefficient

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Multiple Choice

Q 54Q 54

In multiple regression,a dummy variable is significantly related to the dependent variable when ________.
A)the global test of the regression equation is rejected
B)the test of the dummy variable's regression coefficient is rejected
C)the dummy variable is correlated with other independent variables
D)the dummy variable is coded as 2 or 3

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Multiple Choice

Q 55Q 55

Multiple regression analysis is applied when analyzing the relationship between ________.
A)an independent variable and several dependent variables
B)a dependent variable and several independent variables
C)several dependent variables and several independent variables
D)several regression equations and a single sample

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Multiple Choice

Q 56Q 56

In an ANOVA table for a multiple regression analysis,total variation is separated into ________.
A)treatment and error variation
B)regression and residual variation
C)treatment and block variation
D)block and error variation

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Multiple Choice

Q 57Q 57

In an ANOVA table for a multiple regression analysis,the regression mean square is ________.
A)the treatment sum of squares divided by the regression degrees of freedom
B)n − (k + 1)
C)the regression sum of squares divided by the regression degrees of freedom
D)the total sum of squares divided by the regression degrees of freedom

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Multiple Choice

Q 58Q 58

In an ANOVA table for a multiple regression analysis,the global test of significance is based on the ________.
A)treatment mean square divided by the error variation
B)block and error variation
C)treatment mean square and block mean square
D)regression mean square divided by the mean square error

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Multiple Choice

Q 59Q 59

A researcher is studying the relationship between 10 different variables and a critical measure of business performance. What method can be used to select the best set of variables to predict performance?
A)Stepwise regression
B)ANOVA
C)Simple linear regression
D)Residual analysis

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Multiple Choice

Q 60Q 60

A researcher is studying the effect of 10 different variables on a critical measure of business performance. A multiple regression analysis including all 10 variables is performed. What criterion could be used to eliminate 1 of the 10 variables?
A)Multiple R

^{2}B)Largest p-value C)Smallest p-value D)Smallest regression coefficientFree

Multiple Choice

Q 61Q 61

A researcher is studying the effect of 10 different variables on a critical measure of business performance. In selecting the best set of independent variables to predict the dependent variable,the stepwise regression technique is used. How are variables selected for inclusion in the model?
A)Highest increase in the multiple R

^{2}B)Largest p-value C)Smallest p-value D)Smallest regression coefficientFree

Multiple Choice

Q 62Q 62

The following correlations were computed as part of a multiple regression analysis that used education,job,and age to predict income. What is this table called?
A)Net regression coefficients
B)Coefficients of nondetermination
C)Analysis of variance
D)Correlation matrix

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Multiple Choice

Q 63Q 63

The following correlations were computed as part of a multiple regression analysis that used education,job,and age to predict income. Which is the dependent variable?
A)Income
B)Age
C)Education
D)Job

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Multiple Choice

Q 64Q 64

The following correlations were computed as part of a multiple regression analysis that used education,job,and age to predict income. Which independent variable has the strongest association with the dependent variable?
A)Income
B)Age
C)Education
D)Job

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Multiple Choice

Q 65Q 65

The following correlations were computed as part of a multiple regression analysis that used education,job,and age to predict income. Which independent variable has the weakest association with the dependent variable?
A)Income
B)Age
C)Education
D)Job

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Multiple Choice

Q 66Q 66

Twenty-one executives in a large corporation were randomly selected to study the effect of several factors on annual salary (expressed in $000s). The factors selected were age,seniority,years of college,number of company divisions to which they had been exposed,and the level of their responsibility. The results of the regression analysis follow: Which one of the following is the dependent variable?
A)Age
B)Seniority
C)Level of responsibility
D)Annual salary

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Multiple Choice

Q 67Q 67

A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months),gender (0 = female,1 = male),and job type (0 = clerical,1 = technical). The following ANOVA summarizes the regression results: Based on the ANOVA and a 0.05 significance level,the global null hypothesis test of the multiple regression model ________.
A)will be rejected and conclude that monthly salary is related to all of the independent variables
B)will be rejected and conclude that monthly salary is related to at least one of the independent variables
C)will not be rejected
D)will show a high multiple coefficient of determination

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Multiple Choice

Q 68Q 68

A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months),gender (0 = female,1 = male),and job type (0 = clerical,1 = technical). The following ANOVA summarizes the regression results: Based on the ANOVA,the coefficient of multiple determination is ________.
A)5.957%
B)59.3%
C)40.7%
D)cannot be computed

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Multiple Choice

Q 69Q 69

A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months),gender (0 = female,1 = male),and job type (0 = clerical,1 = technical). The following ANOVA summarizes the regression results: Based on the hypothesis tests for the individual regression coefficients,________.
A)all the regression coefficients are not equal to zero
B)"job" is the only significant variable in the model
C)only months of service and gender are significantly related to monthly salary
D)"service" is the only significant variable in the model

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Multiple Choice

Q 70Q 70

A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months),gender (0 = female,1 = male),and job type (0 = clerical,1 = technical). The following ANOVA summarizes the regression results: Based on the hypothesis tests for the individual regression coefficients,________.
A)all the regression coefficients are not equal to zero
B)"job" is the only nonsignificant variable in the model
C)the intercept is the only significant variable in the model
D)"service" is the only significant variable in the model

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Multiple Choice

Q 71Q 71

A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months),gender (0 = female,1 = male),and job type (0 = clerical,1 = technical). The following ANOVA summarizes the regression results: In the regression model,which of the following are dummy variables?
A)Intercept
B)Service
C)Service and gender
D)Gender and job

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Multiple Choice

Q 72Q 72

A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months),gender (0 = female,1 = male),and job type (0 = clerical,1 = technical). The following ANOVA summarizes the regression results: The results for the variable gender show that ________.
A)males average $222.78 more than females in monthly salary
B)females average $222.78 more than males in monthly salary
C)gender is not related to monthly salary
D)gender and months of service are correlated

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Multiple Choice

Q 73Q 73

A multiple regression model includes (X

_{1})(X_{2}). The term is called ________. A)a dependent variable B)an interaction C)an error D)an interceptFree

Multiple Choice

Q 74Q 74

A multiple regression model includes the term (X

_{1})(X_{2}). The term implies that ________. A)the independent variables are correlated B)there is only one independent variable in the regression model C)the effect of X_{1}on the dependent variable is independent of the value of X_{2}D)the effect of X_{1}on the dependent variable may depend on the value of X_{2}Free

Multiple Choice

Q 75Q 75

A multiple regression model includes the term (X

_{1})(X_{2}). If the hypothesis concerning the term's regression coefficient is not rejected,what is a valid conclusion? A)The independent variables are correlated. B)There is only one independent variable in the regression model. C)The effect of X_{1}on the dependent variable is independent of the value of X_{2}. D)The effect of X_{1}on the dependent variable depends on the value of X_{2}.Free

Multiple Choice

Q 76Q 76

A variable that can assume only one of two possible outcomes that take on the values of either 0 or 1,and is used to incorporate the effect of qualitative variables in a regression model,is referred to as ________.
A)a dummy variable
B)a constant endogenous variable
C)an interaction
D)a constant

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Multiple Choice

Q 77Q 77

Consider a regression model involving more than one independent variable. The test used to determine if the relationship between the dependent variable and the set of independent variables is significant is the ________.
A)z-test
B)test
C)chi-square test
D)F-test

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Multiple Choice

Q 78Q 78

Consider a multiple regression analysis involving 14 independent variables and 150 observations,with SSE = 180 and SS Total = 600. The coefficient of multiple determination is ________.
A)0.70
B)0.40
C)0.21
D)0.30

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Multiple Choice

Q 79Q 79

Which of the following statements about stepwise regression is true?
A)It uses only dependent variables and adds them one by one.
B)It uses independent variables with insignificant regression coefficients.
C)It is a step-by-step method that adds independent variables one by one in order to build a more efficient regression equation.
D)It selects the independent variable with the weakest correlation first.

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Multiple Choice

Q 80Q 80

Consider the multiple regression model shown next between the dependent variable Y and four independent variables X

_{1},X_{2},X_{3},and X_{4},which result in the following function: = 33 + 8X_{1}− 6X_{2}+ 16X_{3}+ 18X_{4}For this model,there were 35 observations; SSR = 1,400 and SSE = 600. Assume a 0.01 significance level. Based on the given information,which of the following conclusions is correct? A)Reject the null hypothesis that X_{3}= 0. B)Do not reject the null hypothesis that X_{1}= X_{2}= X_{3}= X_{4}= 0. C)Reject the null hypothesis that X_{1}= 0. D)Reject the null hypothesis that X_{1}= X_{2}= X_{3}= X_{4}= 0.Free

Multiple Choice

Q 81Q 81

Consider the multiple regression model shown next between the dependent variable Y and four independent variables X

_{1},X_{2},X_{3},and X_{4},which result in the following function: = 33 + 8X_{1}− 6X_{2}+ 16X_{3}+ 18X_{4}For this model,there were 35 observations; SSR = 1,400 and SSE = 600. The critical F-value at the 1% level of significance is A)3.83 B)2.61 C)4.02 D)2.53Free

Multiple Choice