Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

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 _____.

Accepted Answer

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

Question 5

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 _____.

Accepted Answer

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

Question 6

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

Accepted Answer

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 
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 7

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

Accepted Answer

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

Question 8

The ratio of MSE/MSR yields _____.

Accepted Answer

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

Question 9

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

Accepted Answer

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 
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 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

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 
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 13

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) _____.

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

The multiple coefficient of determination is _____.

Accepted Answer

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

Question 16

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 _____.

Accepted Answer

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

Question 17

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 _____.

Accepted Answer

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

Question 18

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

Accepted Answer

A)  k − 1 
B)  k 
C)  k + 1 
D)  2k 
A)  k − 1 
B)  k 
C)  k + 1 
D)  2k

Question 19

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

Accepted Answer

A)  the same for all values of the dependent variable 
B)  0 
C)  the same for all values of the independent variable 
D)  -1 
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 20

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 _____.

Accepted Answer

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

Exam 15: Multiple Regression

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

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

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

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

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

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

The ratio of MSE/MSR yields _____.

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

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

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

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

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) _____.

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

The multiple coefficient of determination is _____.

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 _____.

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 _____.

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

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

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

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Inference About Means and Proportions With Two Populations

Inferences About Population Variances

Tests of Goodness of Fit, Independence, and Multiple Proportions

Experimental Design and Analysis of Variance

Simple Linear Regression

Regression Analysis: Model Building

Time Series Analysis and Forecasting

Nonparametric Methods

Statistical Methods for Quality Control

Decision Analysis

Sample Survey

Filters

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 _____.

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 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 _____.