Question 1

Which of the following is not an assumption of the multiple linear regression model?

Accepted Answer

A) Independent error terms. 
B) Population of error terms has a normal distribution. 
C) Populations of error terms observed at different combinations of values of the independent variable (x1,x2,..... ,xk)have equal variances. 
D) The level of measurement of the data for the dependent variable is at least ordinal. 
E) At any combination of values of x1,x2,... ,xk,the population of potential error term values has a mean equal to zero. 
A) Independent error terms. 
B) Population of error terms has a normal distribution. 
C) Populations of error terms observed at different combinations of values of the independent variable (x1,x2,..... ,xk)have equal variances. 
D) The level of measurement of the data for the dependent variable is at least ordinal. 
E) At any combination of values of x1,x2,... ,xk,the population of potential error term values has a mean equal to zero. D

Question 2

Below is a partial multiple regression computer output.

Accepted Answer

$$\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \ \text { Model } & 32,774 & 5 \ \text { Error } & 21,886 & 292 \ \text { Total } & 54,660 & 297 \ & & \ & \text { Coefficient } & \left( s _ { b } \right) \ \text { Variable } & \text { Estimate } & \text { Standard Error } \ \text { Intercept } & 22.02 & \ \mathrm { X } _ { 1 } & - .18 & .04 \ \mathrm { X } _ { 2 } & - .25 & .12 \ \mathrm { X } _ { 3 } & - 4.69 & 1.70 \ \mathrm { X } _ { 4 } & 3.67 & 0.40 \ \mathrm { X } _ { 5 } & 22.32 & 3.60 \end{array}$$ Test the usefulness of variable x₅ in the model at α = .05.Calculate the t statistic and state your conclusions. t = 6.2.We reject H₀ and conclude that x₅ is making a significant contribution in predicting y. Feedback:t for x₅ = 22.32/3.60 = 6.20 t_.025,296 ≈ 1.96 so reject null hypothesis

Question 3

Using squared and interaction variables in a multiple regression model results in extreme multicollinearity.

Accepted Answer

A) True 
 B)False  True

Question 4

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

Accepted Answer

A)  $y _ {i } - \bar { y }$ 
B)  $y _ { i } - \hat { y } _ { i }$ 
C)  $\hat { y } _ { i } - \bar { y }$ 
D)  $\bar { y } - \hat { y } _ { i }$ 
E) None of these 
A)  $y _ {i } - \bar { y }$ 
B)  $y _ { i } - \hat { y } _ { i }$ 
C)  $\hat { y } _ { i } - \bar { y }$ 
D)  $\bar { y } - \hat { y } _ { i }$ 
E) None of these

Question 5

In a multiple regression analysis,the current model has three independent variables.The analyst decides to add another (fourth)independent variable while retaining the other three independent variables.As a result of this addition,the value of MSE will ____________ decrease.

Accepted Answer

A) Always 
B) Sometimes 
C) Never 
A) Always 
B) Sometimes 
C) Never

Question 6

The error term in the regression model describes the effects of all factors other than the independent variables on y (response variable).

Accepted Answer

A) True 
 B)False

Question 7

In the quadratic regression model $\mathrm { y } = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 1 } ^ { 2 } + \varepsilon$
If the term ?2 is ___________ zero,then the parabola opens ____________.

Accepted Answer

A) Less than,upward 
B) Greater than,upward 
C) Greater than,either upward or downward 
D) Less than,either upward or downward 
E) Equal to,downward 
A) Less than,upward 
B) Greater than,upward 
C) Greater than,either upward or downward 
D) Less than,either upward or downward 
E) Equal to,downward

Question 8

Below is a partial multiple regression ANOVA table.

Accepted Answer

\[\begin{array} { l l l } 
\text { Sourc

Question 9

The management of a professional baseball team is in the process of determining the budget for next year.A major component of future revenue is attendance at the home games.In order to predict attendance at home games,the team statistician has used a multiple regression model with dummy variables.The model is of the form y = β0 + β1x1 + β2x2 + β3x3 + ε,where:
y = attendance at a home game.
x1 = current power rating of the team on a scale from 0 to 100 before the game.
x2 and x3 are dummy variables,and they are defined below.
x2 = 1,if weekend,
x2 = 0,otherwise.
x3 = 1,if weather is favorable,
x3 = 0,otherwise.
After collecting the data,based on 30 games from last year,and implementing the above stated multiple regression model,the team statistician obtained the following least squares multiple regression equation:

Accepted Answer

@#LAT-DLM& 
The multiple regression computer outpu

Question 10

The mean square error of a multiple regression model with k independent variables and n observations is __________.

Accepted Answer

A) SSE/n 
B) SSE/[n + (k + 1)] 
C) SSE/[n - (k + 1)] 
D) SSE/(k + 1) 
A) SSE/n 
B) SSE/[n + (k + 1)] 
C) SSE/[n - (k + 1)] 
D) SSE/(k + 1)

Question 11

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

Accepted Answer

A) Constant variance 
B) Independence 
C) Normality 
D) Variance of zero 
E) Mean of zero 
A) Constant variance 
B) Independence 
C) Normality 
D) Variance of zero 
E) Mean of zero

Question 12

Below is a partial multiple regression ANOVA table.

Accepted Answer

\[\begin{array} { l l l } 
\text { Sourc

Question 13

Below is a partial multiple regression ANOVA table.

Accepted Answer

\[\begin{array} { l l l } 
\text { Sourc

Question 14

The multiple correlation coefficient can assume any value between zero and 1,inclusive.

Accepted Answer

A) True 
 B)False

Question 15

Assumptions of a regression model can be evaluated by plotting and analyzing the ____________.

Accepted Answer

A) independent variables 
B) dependent variables 
C) error terms 
D) beta values 
A) independent variables 
B) dependent variables 
C) error terms 
D) beta values

Question 16

Multicollinearity between independent variables is serious if the mean variance inflation factor is:

Accepted Answer

A) Substantially less than 1. 
B) Substantially greater than 1. 
C) Between -1 and +1. 
D) Less than .5. 
E) Substantially less than zero. 
A) Substantially less than 1. 
B) Substantially greater than 1. 
C) Between -1 and +1. 
D) Less than .5. 
E) Substantially less than zero.

Question 17

In a multiple regression model,the residuals were plotted against the values of one of the independent variables.The plot exhibited a funneling out pattern of residuals.This means that as the value of the independent variable increases,the error terms tend to ___________ and the model assumption of __________ is violated.

Accepted Answer

A) increase,constant variance 
B) increase,independence 
C) decrease,constant variance 
D) decrease,normality 
A) increase,constant variance 
B) increase,independence 
C) decrease,constant variance 
D) decrease,normality

Question 18

The management of a professional baseball team is in the process of determining the budget for next year.A major component of future revenue is attendance at the home games.In order to predict attendance at home games,the team statistician has used a multiple regression model with dummy variables.The model is of the form y = β0 + β1x1 + β2x2 + β3x3 + ε,where:
y = attendance at a home game.
x1 = current power rating of the team on a scale from 0 to 100 before the game.
x2 and x3 are dummy variables,and they are defined below.
x2 = 1,if weekend,
x2 = 0,otherwise.
x3 = 1,if weather is favorable,
x3 = 0,otherwise.
After collecting the data,based on 30 games from last year,and implementing the above stated multiple regression model,the team statistician obtained the following least squares multiple regression equation:

Accepted Answer

@#LAT-DLM& 
The multiple regression computer outpu

Question 19

As we increase the number of independent variables in a multiple regression model,the F statistic will __________ increase.

Accepted Answer

A) Always 
B) Sometimes 
C) Never 
A) Always 
B) Sometimes 
C) Never

Question 20

The range of feasible values for the multiple coefficient of determination is from ________.

Accepted Answer

A) 0 to
$\bar{w}$ 
B) -1 to 0 
C) -1 to 1 
D) 0 to 1 
E) - 
A) 0 to
$\bar{w}$ 
B) -1 to 0 
C) -1 to 1 
D) 0 to 1 
E) -

Which of the following is not an assumption of the multiple linear regression model?

Below is a partial multiple regression computer output.

Using squared and interaction variables in a multiple regression model results in extreme multicollinearity.

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

In a multiple regression analysis,the current model has three independent variables.The analyst decides to add another (fourth)independent variable while retaining the other three independent variables.As a result of this addition,the value of MSE will ____________ decrease.

The error term in the regression model describes the effects of all factors other than the independent variables on y (response variable).

In the quadratic regression model $\mathrm { y } = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 1 } ^ { 2 } + \varepsilon$ If the term ?₂ is _ zero,then the parabola opens __.

Below is a partial multiple regression ANOVA table.

The mean square error of a multiple regression model with k independent variables and n observations is __________.

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

Below is a partial multiple regression ANOVA table.

Below is a partial multiple regression ANOVA table.

The multiple correlation coefficient can assume any value between zero and 1,inclusive.

Assumptions of a regression model can be evaluated by plotting and analyzing the ____________.

Multicollinearity between independent variables is serious if the mean variance inflation factor is:

As we increase the number of independent variables in a multiple regression model,the F statistic will __________ increase.

The range of feasible values for the multiple coefficient of determination is from ________.

Statistical Inferences for Population Variances

Experimental Design and Analysis of Variance

Chi-Square Tests

Simple Linear Regression Analysis

Time Series Forecasting and Index Numbers

Process Improvement Using Control Charts

Nonparametric Methods

Decision Theory

Filters

Exam 15: Multiple Regression and Model Building

Which of the following is not an assumption of the multiple linear regression model?

Below is a partial multiple regression computer output.

Using squared and interaction variables in a multiple regression model results in extreme multicollinearity.

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

In a multiple regression analysis,the current model has three independent variables.The analyst decides to add another (fourth)independent variable while retaining the other three independent variables.As a result of this addition,the value of MSE will ____________ decrease.

The error term in the regression model describes the effects of all factors other than the independent variables on y (response variable).

In the quadratic regression model y=β0+β1X1+β2X12+ε\mathrm { y } = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 1 } ^ { 2 } + \varepsilony=β0​+β1​X1​+β2​X12​+ε If the term ?2 is ___________ zero,then the parabola opens ____________.

Below is a partial multiple regression ANOVA table.

The mean square error of a multiple regression model with k independent variables and n observations is __________.

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

Below is a partial multiple regression ANOVA table.

Below is a partial multiple regression ANOVA table.

The multiple correlation coefficient can assume any value between zero and 1,inclusive.

Assumptions of a regression model can be evaluated by plotting and analyzing the ____________.

Multicollinearity between independent variables is serious if the mean variance inflation factor is:

As we increase the number of independent variables in a multiple regression model,the F statistic will __________ increase.

The range of feasible values for the multiple coefficient of determination is from ________.

Statistical Inferences for Population Variances

Experimental Design and Analysis of Variance

Chi-Square Tests

Simple Linear Regression Analysis

Time Series Forecasting and Index Numbers

Process Improvement Using Control Charts

Nonparametric Methods

Decision Theory

Filters

In the quadratic regression model $\mathrm { y } = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 1 } ^ { 2 } + \varepsilon$ If the term ?₂ is _ zero,then the parabola opens __.