Deck 15: Multiple Regression

Question 1

The ratio of MSE/MSR yields _____.

A) SST
B) the F statistic
C) SSR
D) None of the answers is correct.

Answer 1

None of the answers is correct.

Question 2

To test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are _____.

A) 47 and 3
B) 3 and 47
C) 2 and 43
D) 3 and 43

Answer 2

3 and 43

Question 3

A variable that takes on the values of 0 or 1 and is used to incorporate the effect of qualitative variables in a regression model is called a(n) _____.

A) interaction
B) constant variable
C) dummy variable
D) None of the answers is correct.

Answer 3

dummy variable

Question 4

A multiple regression model has _____.

A) only one independent variable
B) more than one dependent variable
C) more than one independent variable
D) at least two dependent variables

Question 5

A variable that cannot be measured in terms of how much or how many but instead is assigned values to represent categories is called a(n) _____.

A) interaction
B) constant variable
C) category variable
D) qualitative variable

Question 6

For a multiple regression model, SSR = 600 and SSE = 200. The multiple coefficient of determination is _____.

A) .333
B) .275
C) .300
D) .75

Question 7

In regression analysis, the response variable is the _____.

A) independent variable
B) dependent variable
C) slope of the regression function
D) intercept

Question 8

In a multiple regression analysis involving 15 independent variables and 200 observations, SST = 800 and SSE = 240. The coefficient of determination is ______.

A) .300
B) .192
C) .500
D) .700

Question 9

In a multiple regression model, the variance of the error term ε is assumed to be _____.

A) the same for all values of the dependent variable
B) 0
C) the same for all values of the independent variable
D) -1

Question 10

If a qualitative variable has k levels, the number of dummy variables required is _____.

A) k − 1
B) k
C) k + 1
D) 2k

Question 11

In regression analysis, an outlier is an observation whose _____.

A) mean is larger than the standard deviation
B) residual is 0
C) mean is 0
D) residual is much larger than the rest of the residual values

Question 12

The numerical value of the coefficient of determination _____.

A) is always larger than the coefficient of correlation
B) is always smaller than the coefficient of correlation
C) is negative if the coefficient of determination is negative
D) can be larger or smaller than the coefficient of correlation

Question 13

The multiple coefficient of determination is _____.

A) MSR/MST
B) MSR/MSE
C) SSR/SST
D) SSE/SSR

Question 14

In a multiple regression model, the error term ε is assumed to be a random variable with a mean of _____.

A) 0
B) -1
C) 1
D) any value

Question 15

In a multiple regression analysis, SSR = 1,000 and SSE = 200. The F statistic for this model is _____.

A) 5.0
B) 1,200
C) 800
D) Not enough information is provided to answer this question.

Question 16

A measure of goodness of fit for the estimated regression equation is the _____.

A) multiple coefficient of determination
B) mean square due to error
C) mean square due to regression
D) sample size

Question 17

The correct relationship between SST, SSR, and SSE is given by _____.

A) SSR = SST + SSE
B) SSR = SST - SSE
C) SSE = SSR - SST
D) None of the answers is correct.

Question 18

A multiple regression model has the form ? $\hat { y }$ = 7 + 2 x₁ + 9 x₂
?
As x₁ increases by 1 unit (holding x₂ constant), $\hat { y }$ is expected to _____.

A) increase by 9 units
B) decrease by 9 units
C) increase by 2 units
D) decrease by 2 units

Question 19

As the goodness of fit for the estimated multiple regression equation increases, _____.

A) the value of the adjusted multiple coefficient of determination decreases
B) the value of the regression equation's constant b₀ decreases
C) the value of the multiple coefficient of determination increases
D) the value of the correlation coefficient increases

Question 20

A regression model involved 5 independent variables and 126 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have _____.

A) 131 degrees of freedom
B) 125 degrees of freedom
C) 130 degrees of freedom
D) 4 degrees of freedom

Question 21

In a multiple regression analysis involving 12 independent variables and 166 observations, SSR = 878 and SSE = 122. The coefficient of determination is _____.

A) .1389
B) .1220
C) .878
D) .7317

Question 22

A variable that cannot be measured in numerical terms is called a _____.

A) non-measurable random variable
B) constant variable
C) dependent variable
D) qualitative variable

Question 23

To test for the significance of a regression model involving 14 independent variables and 255 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are _____.

A) 14 and 255
B) 255 and 14
C) 13 and 240
D) 14 and 240

Question 24

In multiple regression analysis, the correlation among the independent variables is termed _____.

A) homoscedasticity
B) linearity
C) multicollinearity
D) adjusted coefficient of determination

Question 25

In a multiple regression analysis involving 10 independent variables and 81 observations, SST = 120 and SSE = 42. The coefficient of determination is ______.

A) .81
B) .11
C) .35
D) .65

Question 26

In multiple regression analysis, ______.

A) there can be any number of dependent variables but only one independent variable
B) there must be only one independent variable
C) the coefficient of determination must be larger than 1
D) there can be several independent variables, but only one dependent variable

Question 27

A regression model in which more than one independent variable is used to predict the dependent variable is called _____.

A) a simple linear regression model
B) a multiple regression model
C) an independent model
D) None of the answers is correct.

Question 28

A term used to describe the case when the independent variables in a multiple regression model are correlated is _____.

A) regression
B) correlation
C) multicollinearity
D) None of the answers is correct.

Question 29

A regression model involved 18 independent variables and 200 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have _____.

A) 18 degrees of freedom
B) 200 degrees of freedom
C) 199 degrees of freedom
D) 181 degrees of freedom

Question 30

To test for the significance of a regression model involving 8 independent variables and 121 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are _____.

A) 8 and 121
B) 7 and 120
C) 8 and 112
D) 7 and 112

Question 31

For a multiple regression model, SST = 200 and SSE = 50. The multiple coefficient of determination is ______.

A) .25
B) 4.00
C) 250
D) .75

Question 32

In a multiple regression analysis involving 5 independent variables and 30 observations, SSR = 360 and SSE = 40. The coefficient of determination is _____.

A) .80
B) .90
C) .25
D) .15

Question 33

In a residual plot that does not suggest we should challenge the assumptions of our regression model, we would expect to see a _____.

A) horizontal band of points centered near 0
B) widening band of points
C) band of points having a slope consistent with that of the regression equation
D) parabolic band of points

Question 34

A multiple regression model has the form: ? $\hat { y }$ = 5 + 6x + 7w
?
As x increases by 1 unit (holding w constant), y is expected to _____.

A) increase by 11 units
B) decrease by 11 units
C) increase by 6 units
D) decrease by 6 units

Question 35

In a multiple regression model, the values of the error term, ε, are assumed to be _____.

A) 0
B) dependent on each other
C) independent of each other
D) always negative

Question 36

The adjusted multiple coefficient of determination is adjusted for _____.

A) the number of dependent variables
B) the number of independent variables
C) the number of equations
D) detrimental situations

Question 37

In a multiple regression model, the error term ε is assumed to _____.

A) have a mean of 1
B) have a variance of 0
C) have a standard deviation of 1
D) be normally distributed

Question 38

To test for the significance of a regression model involving 4 independent variables and 36 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are _____.

A) 4 and 36
B) 3 and 35
C) 4 and 31
D) 4 and 32

Question 39

A regression analysis involved 6 independent variables and 27 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have _____.

A) 27 degrees of freedom
B) 26 degrees of freedom
C) 21 degrees of freedom
D) 20 degrees of freedom

Question 40

A regression analysis involved 17 independent variables and 697 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have _____.

A) 696 degrees of freedom
B) 16 degrees of freedom
C) 713 degrees of freedom
D) 714 degrees of freedom

Question 41

The mathematical equation that explains how the dependent variable y is related to several independent variables x₁, x₂, ..., xp and the error term ε is a(n) _____.

A) simple nonlinear regression model
B) multiple regression model
C) estimated multiple regression equation
D) multiple regression equation

Question 42

The least squares criterion is _____.

A) min ?(x_i - y_i)²
B) min ?(y_i - $\overline{y}$ _i)²
C) min ?(y_i - $\hat { y }$ _i)²
D) min ?(y_i - $\hat { y }$ _i)

Question 43

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the _____.

A) standard error
B) residual
C) predicted interval
D) variance