Deck 14: Multiple Regression Analysis

Question 1

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

Answer 1

False

Question 2

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

Answer 2

Coefficient of multiple determination

Question 3

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

Answer 3

True

Question 4

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

Question 5

A correlation matrix can be used to assess multicollinearity between independent variables.

Question 6

A correlation matrix shows individual correlation coefficients for all pairs of variables.

Question 7

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

Question 8

In a multiple regression equation with three independent variables,X₁,X₂,and X₃,the interaction term is expressed as (Y)(X₁).

Question 9

An example of a dummy variable is "time to product's first repair" in years.

Question 10

If the hypothesis H₀: β₁ = 0 is rejected,then the sample regression coefficient b₁ indicates the change in the predicted value for a unit change in X₁ when all other X_i variables are held constant.

Question 11

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

Question 12

The coefficient of multiple determination,R²,reports the proportion of the variation in Y that is not explained by the variation in the set of independent variables.

Question 13

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

Question 14

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

Question 15

In multiple regression analysis,an F-statistic is used to test the global hypothesis,H₀: All β_i = 0

Question 16

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

Question 17

Stepwise regression analysis is also called a "backward elimination" method.

Question 18

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

Question 19

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.

Question 20

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

Question 21

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

Question 22

In multiple regression analysis,when the independent variables are highly correlated,this situation is called ________.

A)autocorrelation
B)multicollinearity
C)homoscedasticity
D)curvilinearity

Question 23

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

Question 24

What does the multiple standard error of estimate measure?

A)The change in Ŷ for a change in X₁
B)The variability of the residuals
C)The regression mean square error in the ANOVA table
D)The amount of explained variation

Question 25

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

A)b₁
B)X₁
C)
D)a

Question 26

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.

Question 27

The adjusted R² accounts for the number of independent variables by ________.

A)adding one to the R²
B)using the degrees of freedom
C)multiplying by the multiple standard error of the estimate
D)using a subscript for R²

Question 28

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)

Question 29

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.

Question 30

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

Question 31

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.

Question 32

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

Question 33

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

Question 34

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

A)R² 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 1.0

Question 35

When expressed as a percentage,what is the range of values for multiple R²?

A)−100% to +100% inclusive
B)−100% to 0% inclusive
C)0% to +100% inclusive
D)Unlimited range

Question 36

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.

Question 37

If the coefficient of multiple determination is 0.81,what percent of variation is not explained?

A)19%
B)90%
C)66%
D)81%

Question 38

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

Question 39

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

Question 40

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

Question 41

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

Question 42

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

Question 43

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

Question 44

All other things being held constant,what is the change in the dependent variable for a unit change in X₁ for the multiple regression equation: Ŷ = 5.2 + 6.3X₁ − 7.1 X₂?

A)−7.1
B)+6.3
C)+5.2
D)+4.4

Question 45

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

Question 46

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

Question 47

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 R²
B)Largest p-value
C)Smallest p-value
D)Smallest regression coefficient

Question 48

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

Question 49

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

Question 50

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

Question 51

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

A)H₁: β₁ = β₂ = β₃ = β₄ = 0
B)H₁: β₁ ≠ β₂ ≠ β₃ ≠ β₄ ≠ 0
C)H₁: Not all the β_i's are equal to 0.
D)if F is less than 20.00,then fail to reject.

Question 52

What happens as the scatter of data values about the regression plane increases?

A)The standard error of estimate increases.
B)R² increases.
C)(1 − R²)decreases.
D)The error sum of squares decreases.

Question 53

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

Question 54

Which statistic is used to test a global hypothesis about a multiple regression equation?

A)t-statistic
B)z-statistic
C)^Χ2 (chi-square statistic)
D)F

Question 55

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

Question 56

Which statistic is used to test hypotheses about individual regression coefficients?

A)t-statistic
B)z-statistic
C)^Χ2 (chi-square statistic)
D)F

Question 57

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

A)H₀: β₁ = β₂ = β₃ = β₄ = 0
B)H₀: µ₁ = µ₂ = µ₃ = µ₄ = 0
C)H₀: β₁ = 0
D)if F is greater than 20.00,then reject

Question 58

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

A)H₀: β₁ = β₂ = β₃ = β₄ = 0
B)H₀: µ₁ = µ₂ = µ₃ = µ₄ = 0
C)H₀: β₁ = 0
D)H₀: β₁ ≠ 0

Question 59

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

Question 60

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

Question 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 R²
B)Largest p-value
C)Smallest p-value
D)Smallest regression coefficient

Question 62

Consider the multiple regression model shown next between the dependent variable Y and four independent variables X₁,X₂,X₃,and X₄,which result in the following function: = 33 + 8X₁ − 6X₂ + 16X₃ + 18X₄ 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 X₃ = 0.
B)Do not reject the null hypothesis that X₁ = X₂ = X₃ = X₄ = 0.
C)Reject the null hypothesis that X₁ = 0.
D)Reject the null hypothesis that X₁ = X₂ = X₃ = X₄ = 0.

Question 63

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

Question 64

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

Question 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

Question 66

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

Question 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 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

Question 68

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

Question 69

A multiple regression model includes the term (X₁)(X₂). 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 X₁ on the dependent variable is independent of the value of X₂.
D)The effect of X₁ on the dependent variable depends on the value of X₂.

Question 70

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

Question 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: 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

Question 72

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

Question 73

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

Question 74

A multiple regression model includes (X₁)(X₂). The term is called ________.

A)a dependent variable
B)an interaction
C)an error
D)an intercept

Question 75

A multiple regression model includes the term (X₁)(X₂). 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 X₁ on the dependent variable is independent of the value of X₂
D)the effect of X₁ on the dependent variable may depend on the value of X₂

Question 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

Question 77

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.

Question 78

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

Question 79

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

Question 80

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