Question 1

Given the regression model y = β0 + β1 X1 + β2 X2 + β3 X12 + β4X22 + ε,if we wish to test the significance of higher order terms, (X12 and X22)we would use the following test:

Accepted Answer

A) Overall F test 
B) Durbin-Watson test 
C) Partial F test 
D) t test 
E) Cook's distance measure

Question 2

The standard error decreases if and only if the adjusted multiple coefficient of determination decreases.

Accepted Answer

A) True 
 B)False

Question 3

The manufacturer of a light fixture believes that the dollars spent on advertising,the price of the fixture,and the number of retail stores selling the fixture in a particular month influence the light fixture sales.The manufacturer randomly selects 10 months and collects the following data: $$\begin{array} { l l l l } 
\text { Sales } & \text { Advertising } & \text { Price } & \text { \# of stores } \
41 & 20 & 40 & 1 \
42 & 40 & 60 & 3 \
59 & 40 & 20 & 4 \
60 & 50 & 80 & 5 \
81 & 50 & 10 & 6 \
80 & 60 & 40 & 6 \
100 & 70 & 20 & 7 \
82 & 70 & 60 & 8 \
101 & 80 & 30 & 9 \
110 & 90 & 40 & 10
\end{array}$$ The sales are in thousands of units per month,the advertising is given in hundreds of dollars per month,the price is the unit retail price for the particular month.With this data,the following computer output is obtained.
The regression equation is
Sales = 31.0 + 0.820 Advertising - 0.325 Price + 1.84 Stores $$\begin{array} { l l l l l } 
\text { Predictor } & \text { Coef } & \text { StDev } & \mathrm { T } & \mathrm { P } \
\text { Constant } & 30.992 & 7.728 & 4.01 & 0.007 \
\text { Advertising } & 0.8202 & 0.5023 & 1.63 & 0.154 \
\text { Price } & - 0.32502 & 0.08935 & - 3.64 & 0.011 \
\text { Stores } & 1.841 & 3.855 & 0.48 & 0.650
\end{array}$$ S = 5.465 R-Sq = 96.7% R-Sq(adj)= 95.0%
Analysis of Variance $$\begin{array} { l l l l l l } 
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\text { Regression } & 3 & 5179.2 & 1726.4 & 57.81 & 0.000 \
\text { Residual Error } & 6 & 179.2 & 29.9 & &
\end{array}$$ Based on the multiple regression model given above,the point estimate of the monthly light fixture sales corresponding to second sample data is 49.82 or 49,820 units.This point estimate is calculated based on the assumption that the company spends $4000 on advertising,the price of the fixture is $60,and the fixture is being sold at 3 retail stores.Additional information related to this point estimate is given below. $$\begin{array} { l l l l l l l } 
\text { Obs. } & \text { Advert } & \text { Sales } & \text { Fit } & \text { StDev Fit } & \text { Residual } & \text { St Resid. } \
2 & 40.0 & 42.00 & 49.82 & 3.53 & - 7.82 & - 1.87
\end{array}$$
-Determine the 95% confidence interval for this point estimate and interpret its meaning.

Accepted Answer

The answer of The manufacturer of a light fixture believes...

Question 4

Below is a partial multiple regression ANOVA table.
$$\begin{array} { l l l } 
\text { Source } & \text { SS } & \text { df } \
\text { Model } & 0.242 & 2 \
\text { Error } & 0.105 & 3
\end{array}$$
-What is the total sum of squares (total variation),explained variation,mean square error and the number of observations in the sample?

Accepted Answer

The answer of Below is a partial multiple regression ANOVA...

Question 5

Consider the following partial computer output for a multiple regression model. $$\begin{array} { l l l } 
\text { Predictor } & \text { Coefficient } \left( \mathrm { b } _ { \mathrm { i } } \right) & \text { Standard Dev } \left( \mathrm { s } _ { \mathrm { b } } \right) \
\text { Constant } & 99.3883 & \
\text { X1 } & - 0.007207 & 0.0031 \
\text { X2 } & 0.0011336 & 0.00122 \
\text { X3 } & 0.9324 & 0.373 \
& & \
\text { Analysis of Variance } & & \text { SS } \
\text { Source } & \text { df } & 31.308 \
\text { Regression } & 3 & 9.378
\end{array}$$
-Consider the following analysis of variance table from a multiple regression model.Test the model for overall usefulness at

Accepted Answer

The answer of Consider the following partial computer output for...

Question 6

Below is a partial multiple regression ANOVA table.
$$\begin{array} { l l l } 
\text { Source } & \text { SS } & \text { df } \
\mathrm { X } _ { 1 } & 535.9569 & 1 \
\mathrm { X } _ { 2 } & 1,167.5634 & 1 \
\mathrm { X } _ { 3 } & 18.9886 & 1 \
\text { Error } & 3,459.6803 & 8
\end{array}$$
-What is the total sum of squares (total variation)?

Accepted Answer

A) 535.9569 
B) 1167.5634 
C) 18.9886 
D) 3459.68 
E) 5,182.19

Question 7

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's statistician has used a multiple regression model with dummy variables.The model is of the form: y = βS1U1B10S1U1B0+ βS1U1B11S1U1B0xS1U1B11S1U1B0+ βS1U1B12S1U1B0xS1U1B12S1U1B0+ βS1U1B13S1U1B0xS1U1B13S1U1B0+ 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.
x2and x3are dummy variables,and they are defined below.
x2= 1,if weekend
x2= 0,otherwise
x3= 1,if weather is favourable
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: $$\hat { y } = - 1050 + 250 x _ { 1 } + 2200 x _ { 2 } + 5400 x _ { 3 }$$ The multiple regression compute output also indicated the following: $$s _ { b _ { 1 } } = 800 , s _ { b _ { 2 } } = 1000 , s _ { b _ { 3 } } = 1850$$
-Interpret the estimated model coefficient b1

Accepted Answer

The answer of The management of a professional baseball team...

Question 8

Completely randomized analysis of variance models (one-way ANOVA)can always be converted to a multiple regression models with dummy independent variables.

Accepted Answer

A) True 
 B)False

Question 9

R2is defined as the proportion of the observed variation in the dependent variable that is explained by the fitted regression model.

Accepted Answer

A) True 
 B)False

Question 10

Multicollinearity between independent variables is serious when the correlation between pair(s)of dependent variables is _____.

Accepted Answer

A) close to +/- 1 
B) substantially greater than 1 
C) zero 
D) substantially less than zero

Question 11

Given the regression model y = β0+ β1X1+ β2X12+ ε,if we wish to test the significance of X12,the appropriate null hypothesis is:

Accepted Answer

A) H0: X12= 0 
B) H0: β2≠ 0 
C) H0: β2≠ X12 
D) H0: β2= 0 
E) H0: β2- X12= 0

Question 12

Inclusion of redundant independent variables in the regression model increases the problem of __________.

Accepted Answer

The answer of Inclusion of redundant independent variables in the...

Question 13

In a regression equation,beta values are previously known parameter values.

Accepted Answer

A) True 
 B)False

Question 14

In the quadratic regression model y = ?₀+ ?₁x + ?₂x²+ ?,if the value of the term ?₁increases,then the parabola shifts to the _________.

Accepted Answer

The answer of In the quadratic regression model y =...

Question 15

Below is a partial multiple regression computer output.
$$\begin{array} { l l l } 
\text { Source } & \text { SS } & \text { df } \
\text { Model } & 32,774 & 5 \
\text { Error } & 21,886 & 292 \
\text { Total } & 54,660 & 297
\end{array}$$
-Test the overall usefulness of the model at

Accepted Answer

The answer of Below is a partial multiple regression computer...

Question 16

Write the least squares prediction equation.

Accepted Answer

The answer of Write the least squares prediction equation....

Question 17

Determine the 95% interval for β₂ and interpret its meaning

Accepted Answer

The answer of Determine the 95% interval for β₂ and...

Question 18

Below is a partially completed multiple regression analysis of variance (ANOVA)table.What is the value of R2? $$\begin{array} { l l l } 
\text { Source } & \text { SS } & \text { df } \
\text { Model } & 32,774 & 5 \
\text { Error } & 21,886 & 292
\end{array}$$

Accepted Answer

A) .19 
B) .60 
C) .32 
D) .48 
E) .56

Question 19

Test the usefulness of variable x₂ in the model at

Accepted Answer

The answer of Test the usefulness of variable x₂ in...

Question 20

Below is a partial multiple regression computer output.
$$\begin{array} { l l l } 
\text { Source } & \text { SS } & \text { df } \
\text { Model } & 32,774 & 5 \
\text { Error } & 21,886 & 292 \
\text { Total } & 54,660 & 297
\end{array}$$
-What is the number of independent variables in the model?

Accepted Answer

A) 1 
B) 2 
C) 3 
D) 4 
E) 5

Exam 12: Multiple Regression and Model Building

Given the regression model y = β₀ + β₁ X₁ + β₂ X₂ + β₃ X₁² + β₄X₂² + ε,if we wish to test the significance of higher order terms, (X₁² and X₂²) we would use the following test:

The standard error decreases if and only if the adjusted multiple coefficient of determination decreases.

Completely randomized analysis of variance models (one-way ANOVA)can always be converted to a multiple regression models with dummy independent variables.

R²is defined as the proportion of the observed variation in the dependent variable that is explained by the fitted regression model.

Multicollinearity between independent variables is serious when the correlation between pair(s) of dependent variables is _____.

Given the regression model y = β₀+ β₁X₁+ β₂X₁²+ ε,if we wish to test the significance of X₁²,the appropriate null hypothesis is:

Inclusion of redundant independent variables in the regression model increases the problem of __________.

In a regression equation,beta values are previously known parameter values.

In the quadratic regression model y = ?₀+ ?₁x + ?₂x²+ ?,if the value of the term ?₁increases,then the parabola shifts to the _________.

Below is a partial multiple regression computer output. $\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \\\text { Model } & 32,774 & 5 \\\text { Error } & 21,886 & 292 \\\text { Total } & 54,660 & 297\end{array}$ -Test the overall usefulness of the model at

Write the least squares prediction equation.

Determine the 95% interval for β₂ and interpret its meaning

Below is a partially completed multiple regression analysis of variance (ANOVA) table.What is the value of R²? $\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \\\text { Model } & 32,774 & 5 \\\text { Error } & 21,886 & 292\end{array}$

Test the usefulness of variable x₂ in the model at

Below is a partial multiple regression computer output. $\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \\\text { Model } & 32,774 & 5 \\\text { Error } & 21,886 & 292 \\\text { Total } & 54,660 & 297\end{array}$ -What is the number of independent variables in the model?

Exam 12: Multiple Regression and Model Building

Given the regression model y = β0 + β1 X1 + β2 X2 + β3 X12 + β4X22 + ε,if we wish to test the significance of higher order terms, (X12 and X22) we would use the following test:

The standard error decreases if and only if the adjusted multiple coefficient of determination decreases.

Completely randomized analysis of variance models (one-way ANOVA)can always be converted to a multiple regression models with dummy independent variables.

R2is defined as the proportion of the observed variation in the dependent variable that is explained by the fitted regression model.

Multicollinearity between independent variables is serious when the correlation between pair(s) of dependent variables is _____.

Given the regression model y = β0+ β1X1+ β2X12+ ε,if we wish to test the significance of X12,the appropriate null hypothesis is:

Inclusion of redundant independent variables in the regression model increases the problem of __________.

In a regression equation,beta values are previously known parameter values.

In the quadratic regression model y = ?0+ ?1x + ?2x2+ ?,if the value of the term ?1increases,then the parabola shifts to the _________.

Write the least squares prediction equation.

Determine the 95% interval for β2 and interpret its meaning

Test the usefulness of variable x2 in the model at

Given the regression model y = β₀ + β₁ X₁ + β₂ X₂ + β₃ X₁² + β₄X₂² + ε,if we wish to test the significance of higher order terms, (X₁² and X₂²) we would use the following test:

R²is defined as the proportion of the observed variation in the dependent variable that is explained by the fitted regression model.

Given the regression model y = β₀+ β₁X₁+ β₂X₁²+ ε,if we wish to test the significance of X₁²,the appropriate null hypothesis is:

In the quadratic regression model y = ?₀+ ?₁x + ?₂x²+ ?,if the value of the term ?₁increases,then the parabola shifts to the _________.

Determine the 95% interval for β₂ and interpret its meaning

Test the usefulness of variable x₂ in the model at