Deck 14: Multiple Regression Analysis

Question 1

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

Answer 1

True

Question 2

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

Answer 2

True

Question 3

In multiple regression, the multiple R² measures the proportion of ____________.

Answer 3

explained variation in the dependent variable

Question 4

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

Question 5

In multiple regression analysis, the ________ scale is used to measure a dummy variable.

Question 6

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

Question 7

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 8

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

Question 9

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

Question 10

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

Question 11

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

Question 12

In multiple regression, the ________ is used to test the global hypothesis.

Question 13

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

Question 14

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

Question 15

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

Question 16

In multiple regression, the ______________ summarizes the difference between the predicted and actual values of the dependent variable.

Question 17

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 18

In multiple regression analysis, an F-statistic is used to test the global hypothesis, H₀: .

Question 19

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

Question 20

Correlation among successive observations of the dependent variable is called ________________.

Question 21

In the ANOVA table for a multiple regression analysis, the regression degrees of freedom is equal to ___________________.

Question 22

When the variance of the differences between the actual and the predicted values of the dependent variable are approximately the same for all values of the independent variable, the differences are said to exhibit ______________.

Question 23

If the null hypothesis, H₀: β₁ = 0, is rejected, the independent variable, X₁, it has a ______ effect on the dependent variable.

Question 24

In an ANOVA for a multiple regression analysis, the three sources of variation are __________________.

Question 25

The stepwise regression procedure is also called ________.

Question 26

In a multiple regression analysis with five independent variables, the null hypothesis, H₀: β₄ = 0, is not rejected. When predicting the dependent variable, the independent variable, X₄, has ______ relationship to the dependent variable.

Question 27

In a multiple regression analysis, the statistic used to evaluate the presence of correlated independent variables is __________________.

Question 28

Given a multiple linear regression equation, Ŷ = 5.1 + 2.2X₁ - 3.5X₂ (assuming other things are held constant), for a unit increase in the independent variable, X₂, will decrease by _______ units.

Question 29

A __________ analysis is used to develop an equation that predicts an outcome based on two or more independent variables.

Question 30

If a dependent variable and one of the independent variables are inversely related, the sign for the regression coefficient of the independent variable is ____________.

Question 31

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 32

The ___ test statistic is used to test the significance of (X₁)(X₂) in a multiple regression model.

Question 33

In multiple regression analysis, a correlation matrix is used to check for ___________.

Question 34

When applying stepwise regression, the basis for including an independent variable in a multiple regression model is __________.

Question 35

When evaluating the assumptions of a multiple regression model, a _______ is calculated for every observation in a data set.

Question 36

When applying the stepwise regression technique, _________ independent is included in the first multiple regression model.

Question 37

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 38

In multiple regression analysis, a dummy variable is coded as a _______.

Question 39

In a multiple regression model, the ____ test statistic is used to test the significance of an independent variable's regression coefficient.

Question 40

A multiple regression model includes three independent variables: X₁, X₂, and (X₁)(X₂). (X₁)(X₂) is called the ________________________.

Question 41

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 42

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 43

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 44

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

Question 45

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 46

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

A) Autocorrelation
B) Multicollinearity
C) Homoscedasticity
D) Curvilinearity

Question 47

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 48

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 49

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 50

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 51

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 52

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 53

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 54

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 55

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 56

What does the multiple standard error of estimate measure?

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

Question 57

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 autocorrelated

Question 58

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 59

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 60

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

A) b₁
B) X₁
C) Ŷ
D) a

Question 61

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 62

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's are equal to 0.
D) If F is less than 20.00, then fail to reject.

Question 63

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 64

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 65

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 66

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 67

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 68

In multiple regression analysis, residuals (Y - Ŷ) 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 69

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 70

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 71

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 72

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 73

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 74

In multiple regression analysis, residuals (Y - Ŷ) 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 75

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 76

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 77

In multiple regression analysis, residuals (Y - Ŷ) should be ____________.

A) Qualitative variables
B) Significantly different from zero
C) Correlated
D) Normally distributed with a mean of zero

Question 78

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 79

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 80

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 net regression coefficients is not equal to zero.
D) Good predictions are not possible.