Question 1

The graph of the prediction equation obtained from the model y = β₀ + β₁X₁ + β₂X₂ + ε is a(n) ________. A) line B) plane C) parabola D) exponential curve

Accepted Answer

Two independent variables indicate the graph of a plane.

Question 2

In a multiple regression analysis, if the normal probability plot ________, then it can be concluded that the assumption of normality is not violated.
A) is a straight line
B) has the shape of a symmetric bell-shaped curve
C) is greatly curved
D) is left skewed
E) has the shape of a parabola that opens upward

Accepted Answer

A straight line on a normal probability plot shows that the assumption of normality is not violated.

Question 3

In multiple regression analysis, the mean square regression divided by mean square error yields the ________. A) standard error B) F statistic C) R² D) adjusted R² or R⁻² E) t statistic

Accepted Answer

F = MSR/MSE

Question 4

In regression analysis, the standard error(s) is ________ greater than the standard deviation of y, the dependent variable.
A) always
B) sometimes
C) never

Accepted Answer

Because standard deviation is divided by sample size to obtain standard error, standard deviation can never be smaller than standard error.

Question 5

If we are testing the significance of the independent variable X₁ and we reject the null hypothesis H₀: β₁ = 0, we conclude that A) X₁ is significantly related to y. B) X₁ is not significantly related to y. C) X₁ is an unimportant independent variable. D) β₁ is significantly related to the dependent variable y.

Accepted Answer

Rejecting the null hypothesis indicates a significant relationship between an independent and dependent variable.

Question 6

In using the multiple regression method, we can model the effects of the different levels of a qualitative independent variable by using a(n) ________.
A) interaction variable
B) cross-product term
C) quadratic term
D) dummy (indicator) variable
E) variance equalizing transformation

Accepted Answer

Use a dummy (indicator) variable for different levels of a qualitative independent variable in multiple regression.

Question 7

An investigator hired by a client suing for sex discrimination has developed a multiple regression model for employee salaries for the company in question. In this multiple regression model, the salaries are in thousands of dollars. For example, a data entry of 35 for the dependent variable indicates a salary of $35,000. The indicator (dummy) variable for gender is coded as X₁ = 0 if male and X₁ = 1 if female. The computer output of this multiple regression model shows that the coefficient for this variable (X₁) is −4.2. The t test showed that X₁ was significant at α = .1. This result implies that for male and female workers of the company, A) on the average, females earn $4,200 less than males. B) on the average, males earn $4,200 less than females. C) on the average, salaries do not differ between males and females. D) on the average, males have 4.2 more years of experience than females. E) on the average, females have 4.2 more years of experience than males.

Accepted Answer

-4.2 means that females earn $4,200 less than males.

Question 8

Which one of the following is not an assumption about the residuals in a regression model?
A) constant variance
B) independence
C) normality
D) variance of zero
E) mean of zero

Accepted Answer

A variance of zero is not an assumption about the residuals in a regression model.

Question 9

The multiple ________ measures the proportion of the variation in y, the response variable, explained by the multiple regression model or the set of independent variables included in the multiple regression equation.
A) correlation coefficient
B) coefficient of determination
C) total variation
D) standard error
E) F test

Accepted Answer

The multiple coefficient of determination measures the proportion of the variation in y, the response variable, explained by the multiple regression model or the set of independent variables included in the multiple regression equation.

Question 10

Dummy or indicator variables typically are values of zero or one and are used to model the effects of different levels of ________ variables.
A) qualitative
B) quantitative
C) ratio
D) measured

Accepted Answer

Use dummy (indicator) variables for different levels of qualitative data.

Question 11

The y-intercept, β_0, in a multiple regression model represents the estimated value of the ________ variable, when the value of all independent variables are ________. A) response, one B) dummy, zero C) response, zero D) dummy, one

Accepted Answer

When the independent variables are 0, they "disappear," leaving just the value of the y-intercept.

Question 12

The ________ term describes the effects on y of all factors other than the independent variables in a multiple regression model.
A) dependent
B) t test
C) error
D) dummy

Accepted Answer

The error term describes the effects on y of all factors other than the independent variables in a multiple regression model.

Question 13

In multiple regression analysis, the explained sum of squares divided by the total sum of squares yields the ________. A) standard error B) F statistic C) R² D) adjusted R² or R⁻² E) t statistic

Accepted Answer

R² = (SSE/SST)

Question 14

The effects of different levels of qualitative independent variables are described using ________ variables.
A) dependent
B) response
C) dummy
D) quantitative

Accepted Answer

Dummy (indicator) variables are used for qualitative data.

Question 15

Which of the following residual plots is not used in regression analysis?
A) residuals vs. parameter estimates
B) residuals vs. values of an independent variable
C) residuals vs. time order
D) residuals vs. predicted values of the dependent variable
E) standardized residuals vs. predicted values of the dependent variable

Accepted Answer

All of these are used in regression analysis except residuals vs. parameter estimates.

Question 16

R² is defined as A) total variation/explained variation. B) explained variation/total variation. C) unexplained variation/explained variation. D) unexplained variation/total variation.

Accepted Answer

R² = (explained variation)/(total variation)

Question 17

In multiple regression analysis, a desirable residual plot has what type of appearance?
A) curved
B) cyclical
C) fanning out
D) funneling in
E) horizontal band

Accepted Answer

A horizontal band is the desired residual plot in multiple regression analysis.

Question 18

An acceptable residual plot exhibits
A) increasing error variance.
B) decreasing error variance.
C) constant error variance.
D) a curved pattern.
E) a mixture of increasing and decreasing error variance.

Accepted Answer

Error variance should be constant in a residual plot.

Question 19

Which one of the following tools is not used to check the normality of residuals assumption for a multiple regression model?
A) histogram
B) stem-and-leaf display
C) scatter diagram
D) normal plot

Accepted Answer

Use any of these EXCEPT a scatter diagram to check the normality of residuals assumption.

Question 20

In multiple regression analysis, which one of the following is the appropriate notation for error, or residual?
A)  −

B)  −

C)  −

D)  −

E) None of these answers is correct.

Accepted Answer

A residual is the difference between the observed and predicted values.

Quiz 15: Multiple Regression and Model Building

The graph of the prediction equation obtained from the model y = β₀ + β₁X₁ + β₂X₂ + ε is a(n) ________.

In a multiple regression analysis, if the normal probability plot ________, then it can be concluded that the assumption of normality is not violated.

In multiple regression analysis, the mean square regression divided by mean square error yields the ________.

In regression analysis, the standard error(s) is ________ greater than the standard deviation of y, the dependent variable.

If we are testing the significance of the independent variable X₁ and we reject the null hypothesis H₀: β₁ = 0, we conclude that

In using the multiple regression method, we can model the effects of the different levels of a qualitative independent variable by using a(n) ________.

Which one of the following is not an assumption about the residuals in a regression model?

The multiple ________ measures the proportion of the variation in y, the response variable, explained by the multiple regression model or the set of independent variables included in the multiple regression equation.

Dummy or indicator variables typically are values of zero or one and are used to model the effects of different levels of ________ variables.

The y-intercept, β_0, in a multiple regression model represents the estimated value of the variable, when the value of all independent variables are .

The ________ term describes the effects on y of all factors other than the independent variables in a multiple regression model.

In multiple regression analysis, the explained sum of squares divided by the total sum of squares yields the ________.

The effects of different levels of qualitative independent variables are described using ________ variables.

Which of the following residual plots is not used in regression analysis?

R² is defined as

In multiple regression analysis, a desirable residual plot has what type of appearance?

An acceptable residual plot exhibits

Which one of the following tools is not used to check the normality of residuals assumption for a multiple regression model?

In multiple regression analysis, which one of the following is the appropriate notation for error, or residual?