Deck 14: Multiple Regression Analysis

Question 1

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

Answer 1

autocorrelation

Question 2

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

Answer 2

True

Question 3

To test the global hypothesis in multiple regression analysis, an F-statistic is used.

Answer 3

True

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

In multiple regression, what statistic accounts for the variance of additional independent variables? _____________

Question 9

For a global test of a multiple regression equation, the F-statistic is based on the regression and residual degrees of freedom.

Question 10

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 11

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

Question 12

In multiple regression, what statistic summarizes the difference between the predicted and actual values of the dependent variable? __________________

Question 13

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

Question 14

In multiple regression, what is the form of the global hypothesis test? _____________

Question 15

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

Question 16

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

Question 17

If the hypothesis, H_o: $\beta$ ₁= 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 18

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

Question 19

In multiple regression, the Multiple measures the proportion of _____________.

Question 20

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

Question 21

In a multiple regression analysis ANOVA table, what determines the degrees of freedom associated with the regression sum of squares? ___________________

Question 22

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

Question 23

What test statistic is used to test the significance of (X₁)(X₂) in a multiple regression model? _____________________

Question 24

When applying Stepwise Regression, what is the basis for including an independent variable in a multiple regression model? _____________

Question 25

What analysis is used to develop an equation to predict an outcome based on two or more variables? _____________

Question 26

In multiple regression analysis, what scale is used to measure a dummy variable? _________________________

Question 27

Given a multiple linear regression equation = 5.1 + 2.2X₁ - 3.5X₂, what will a unit increase in the independent variable, X₂, mean in the change of assuming other things are held constant? ________

Question 28

In a multiple regression analysis, how many sources of variation are listed? Name the sources of variation. _____________

Question 29

In a multiple regression analysis, what statistic is used to test for correlated independent variables? ___________________

Question 30

What test statistic is used to test the significance of an independent variable in a multiple regression model? ______

Question 31

When evaluating the assumptions of a multiple regression model, what additional variable is calculated for every observation in a data set? ________________

Question 32

When applying Stepwise Regression, how many independent variables are included in the first multiple regression model? _____________

Question 33

If a dependent variable and one or more independent variables are inversely related, what is the sign for the regression coefficients of the independent variables? ______________

Question 34

The Stepwise Regression procedure is also called __________.

Question 35

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

Question 36

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

Question 37

When the variance of the differences between the actual and the predicted values of the dependent variable are approximately the same, the variables are said to exhibit ______________________________.

Question 38

If the null hypothesis, H_o: $\beta$ ₄ = 0, is not rejected, what effect does the independent variable, X₄, have when predicting the dependent variable? ______

Question 39

If the null hypothesis, H_o: $\beta$ ₁ = 0, is rejected, what effect does the independent variable, X₁, have when predicting the dependent variable? ______

Question 40

In multiple regression, what statistic is used to test the global hypothesis? _____________

Question 41

When does multicollinearity occur in a multiple regression analysis?

A) The dependent variables are highly correlated.
B) The regression coefficients are correlated.
C) The independent variables are highly correlated.
D) The independent variables have no correlation.

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

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

A) the 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 44

To evaluate the assumption of linearity, a multiple regression analysis should include

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 45

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

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

Question 46

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) binomial distribution

Question 47

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 48

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 49

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

A) b₁
B) X₁
C) Ŷ
D) a

Question 50

What does the multiple standard error of estimate measure?

A) Change in for a change in X₁
B) The "error" or variability in predicting Y
C) The regression mean square error in the ANOVA table
D) Amount of explained variation

Question 51

If a multiple regression analysis is based on ten independent variables collected from a sample of 125 observations, what will be the value of the denominator in the calculation of the multiple standard error of estimate?

A) 125
B) 10
C) 114
D) 115

Question 52

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 53

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 54

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 55

The variance inflation factor can be used to

A) select or eliminate variables for a multiple regression model.
B) evaluate homoscedasticity.
C) evaluate the distribution of residuals.
D) test null hypothesis that all regression coefficients equal zero must be rejected.

Question 56

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 57

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) prediction error is minimized

Question 58

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

In a multiple regression ANOVA table, explained variation 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 60

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 61

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

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

Question 62

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.

Question 63

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 64

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 65

All other things being held constant, what is the change in the dependent variable for a unit change in the first independent variable 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 66

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 67

The degrees of freedom associated with the regression sum of squares equals

A) the number of independent variables
B) 1
C) F-ratio
D) (n - 2)

Question 68

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 69

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 70

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

A) Standard error of estimate increases
B) R² increases
C) (1 - R²) decreases
D) Error sum of squares decreases

Question 71

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 72

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 73

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

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

Question 74

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 75

In a regression analysis, three independent variables are used in the equation based on a sample of forty observations. 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 76

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

A) H₀: $\beta$ ₁ = $\beta$ ₂ = $\beta$ ₃ = $\beta$ ₄ = 0
B) H₀: µ₁ = µ₂ = µ₃ = µ₄ = 0
C) H₀: $\beta$ ₁ = 0
D) H₀: $\beta$ ₁ $\neq$ 0

Question 77

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 78

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

A) H₀: $\beta$ ₁ = $\beta$ ₂ = $\beta$ ₃ = $\beta$ ₄ = 0
B) H₀: µ₁ = µ₂ = µ₃ = µ₄ = 0
C) H₀: $\beta$ ₁ = 0
D) If F is greater than 20.00 then reject.

Question 79

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 80

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

A) H₁: $\beta$ ₁ = $\beta$ ₂ = $\beta$ ₃ = $\beta$ ₄ = 0
B) H₁: $\beta$ ₁ $\neq$$\beta$ ₂ $\neq$$\beta$ ₃ $\neq$$\beta$ ₄ $\neq$
C) H₁: Not all the $\beta$ 's are equal to 0
D) If F is less than 20.00 then fail to reject.