Question 1

A multiple linear regression analysis involving 45 observations resulted in the following least squares prediction equation: $$\hat { y } = .408 + 1.3387 x _ { 1 } + 2.1 x _ { 2 }$$ .
The SSE for the above model is 49.
Addition of two other independent variables to the model,resulted in the following multiple linear regression equation: $$\hat { y } = 1.2 + 3 x _ { 1 } + 12 x _ { 2 } + 4 x _ { 3 } + 8 x _ { 4 }$$ .
The latter model's SSE is 40.
-Determine the degrees of freedom regression (explained variation),degrees of freedom error (unexplained variation),and total degrees of freedom for the model with two independent variables.

Accepted Answer

The answer of A multiple linear regression analysis involving 45...

Question 2

The analyst performing the study wants to determine if at least one of the two new independent variables makes a significant contribution to the multiple regression model.State the appropriate null and alternative hypotheses.

Accepted Answer

The answer of The analyst performing the study wants to...

Question 3

Use the following correlation matrix and determine the best multiple regression prediction equation that has no significant multicollinearity.

Accepted Answer

The answer of Use the following correlation matrix and determine...

Question 4

A multiple linear regression analysis involving 45 observations resulted in the following least squares prediction equation: $$\hat { y } = .408 + 1.3387 x _ { 1 } + 2.1 x _ { 2 }$$ .
The SSE for the above model is 49.
Addition of two other independent variables to the model,resulted in the following multiple linear regression equation: $$\hat { y } = 1.2 + 3 x _ { 1 } + 12 x _ { 2 } + 4 x _ { 3 } + 8 x _ { 4 }$$ .
The latter model's SSE is 40.
-Determine the degrees of freedom regression (explained variation),degrees of freedom error (unexplained variation),and total degrees of freedom for the latter model (the model with four independent variables).

Accepted Answer

The answer of A multiple linear regression analysis involving 45...

Question 5

Consider the following partial computer output for a multiple regression model. $$\begin{array} { l c c } 
\text { Predictor } & \text { Coefficient } & \text { Standard Deviation } \
\text { Constant } & 41.225 & 6.380 \
\mathrm { X } _ { 1 } & 1.081 & 1.353 \
\mathrm { X } _ { 2 } & - 18.404 & 4.547
\end{array}$$ Analysis of Variance $$\begin{array} { l r c } 
\text { Source } & \underline { \mathrm { DF } } & \underline { \mathrm { SS } } \
\text { Regression } & 2 & 2270.11 \
\text { Error (residual) } & 26 & 3585.75
\end{array}$$
-What is the total sum of squares (total variation)?

Accepted Answer

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

Question 6

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: $$s _ { b _ { 1 } } = 800 , s _ { b _ { 2 } } = 1000 , s _ { b _ { 3 } } = 1850$$
-Assume that the overall model is useful in predicting the game attendance and the team statistician wants to know if the mean attendance is higher on the weekends as compared to the weekdays.At alpha = .05,test to determine if the attendance is higher on weekend home games.

Accepted Answer

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

Question 7

Consider the following partial computer output for a multiple regression model. $$\begin{array} { l c c } 
\text { Predictor } & \text { Coefficient } & \text { Standard Deviation } \
\text { Constant } & 41.225 & 6.380 \
\mathrm { X } _ { 1 } & 1.081 & 1.353 \
\mathrm { X } _ { 2 } & - 18.404 & 4.547
\end{array}$$ Analysis of Variance $$\begin{array} { l r c } 
\text { Source } & \underline { \mathrm { DF } } & \underline { \mathrm { SS } } \
\text { Regression } & 2 & 2270.11 \
\text { Error (residual) } & 26 & 3585.75
\end{array}$$
-What is the mean square error?

Accepted Answer

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

Question 8

A county has four major hospitals: 1)Regional Memorial;2)General;3)Charity;and 4)City.A multiple regression model is used to compare the time spent in the hospital after a heart by-pass surgery among the four hospitals.The response variable is the amount of time spent in the hospital (in days),the quantitative independent variables include the age of the patient,cholesterol level of the patient,and blood pressure of the patient.Define the dummy variables so that all other hospitals are compared to the City hospital (base).

Accepted Answer

The answer of A county has four major hospitals: 1)Regional...

Question 9

Consider the following partial computer output for a multiple regression model. $$\begin{array} { l c c } \text { Predictor } & \text { Coefficient } & \text { Standard Deviation } \ \text { Constant } & 41.225 & 6.380 \ \mathrm { X } _ { 1 } & 1.081 & 1.353 \ \mathrm { X } _ { 2 } & - 18.404 & 4.547 \end{array}$$ Analysis of Variance $$\begin{array} { l r c } \text { Source } & \underline { \mathrm { DF } } & \underline { \mathrm { SS } } \ \text { Regression } & 2 & 2270.11 \ \text { Error (residual) } & 26 & 3585.75 \end{array}$$ -Calculate R².

Accepted Answer

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

Question 10

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: $$s _ { b _ { 1 } } = 800 , s _ { b _ { 2 } } = 1000 , s _ { b _ { 3 } } = 1850$$
-Assume that the overall model is useful in predicting the game attendance.Assume today is Wednesday morning and the weather forecast indicates sunny,excellent weather conditions for the rest of the day.Later today,there is a home baseball game for this team.Assume that the current power rating of the team is 85 and predict the attendance for today's game.

Accepted Answer

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

Question 11

A multiple regression model with four independent variables consists of 29 observations.The multiple coefficient of determination is R²= .80 and the standard error is s = 2.0.Complete the analysis of variance table for this model and test the overall model for significance.

Accepted Answer

The answer of A multiple regression model with four independent...

Question 12

A multiple regression model with 3 independent variables and 16 observations produced the following results: SSE = 15 and R²= 2/3.Complete the analysis of variance table and calculate the F statistic.

Accepted Answer

The answer of A multiple regression model with 3 independent...

Question 13

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: $$s _ { b _ { 1 } } = 800 , s _ { b _ { 2 } } = 1000 , s _ { b _ { 3 } } = 1850$$
-Assume that the overall model is useful in predicting the game attendance and the team statistician wants to know if the mean attendance is higher on the weekends as compared to the weekdays.State the appropriate null and alternative hypotheses.

Accepted Answer

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

Question 14

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: $$s _ { b _ { 1 } } = 800 , s _ { b _ { 2 } } = 1000 , s _ { b _ { 3 } } = 1850$$
-Assume today is Saturday morning and the weather forecast indicates sunny,excellent weather conditions for the rest of the day and that the overall model is useful in predicting the game attendance.Later today,there is a home baseball game for this team.If the current power rating of the team is 92,use the model given above and predict the attendance for today's game.

Accepted Answer

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

Question 15

At$\alpha$ = .05 test to determine if at least one of the two new independent variables make a significant contribution to the multiple regression model.

Accepted Answer

The answer of At$\alpha$ = .05 test to determine if...

Question 16

A multiple regression model with 3 independent variables and 16 observations produced the following analysis of variance table.

Accepted Answer

The answer of A multiple regression model with 3 independent...

Question 17

A county has four major hospitals: 1)Regional Memorial;2)General;3)Charity;and 4)City.A multiple regression model is used to compare the time spent in the hospital after a heart by-pass surgery among the four hospitals.The response (dependent)variable is the amount of time spent in the hospital (in days).The variables used to predict the time spent in the hospital include the patient's age,cholesterol level (in mlg. ),blood pressure,as well as variables indicating the hospital in which the surgery was performed.Determine the total number of independent variables in the multiple regression model.Indicate how many of these are quantitative variables and how many are indicator (dummy)variables.

Accepted Answer

The answer of A county has four major hospitals: 1)Regional...

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'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 b2.

Accepted Answer

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

Question 19

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 b3.

Accepted Answer

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

Question 20

Consider the following partial computer output for a multiple regression model. $$\begin{array} { l c c } 
\text { Predictor } & \text { Coefficient } & \text { Standard Deviation } \
\text { Constant } & 41.225 & 6.380 \
\mathrm { X } _ { 1 } & 1.081 & 1.353 \
\mathrm { X } _ { 2 } & - 18.404 & 4.547
\end{array}$$ Analysis of Variance $$\begin{array} { l r c } 
\text { Source } & \underline { \mathrm { DF } } & \underline { \mathrm { SS } } \
\text { Regression } & 2 & 2270.11 \
\text { Error (residual) } & 26 & 3585.75
\end{array}$$
-What is the explained variation?

Accepted Answer

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

Quiz 12: Multiple Regression and Model Building

The analyst performing the study wants to determine if at least one of the two new independent variables makes a significant contribution to the multiple regression model.State the appropriate null and alternative hypotheses.

Use the following correlation matrix and determine the best multiple regression prediction equation that has no significant multicollinearity.

A multiple regression model with four independent variables consists of 29 observations.The multiple coefficient of determination is R²= .80 and the standard error is s = 2.0.Complete the analysis of variance table for this model and test the overall model for significance.

A multiple regression model with 3 independent variables and 16 observations produced the following results: SSE = 15 and R²= 2/3.Complete the analysis of variance table and calculate the F statistic.

At $\alpha$ = .05 test to determine if at least one of the two new independent variables make a significant contribution to the multiple regression model.

A multiple regression model with 3 independent variables and 16 observations produced the following analysis of variance table.

Quiz 12: Multiple Regression and Model Building

The analyst performing the study wants to determine if at least one of the two new independent variables makes a significant contribution to the multiple regression model.State the appropriate null and alternative hypotheses.

Use the following correlation matrix and determine the best multiple regression prediction equation that has no significant multicollinearity.

A multiple regression model with four independent variables consists of 29 observations.The multiple coefficient of determination is R2= .80 and the standard error is s = 2.0.Complete the analysis of variance table for this model and test the overall model for significance.

A multiple regression model with 3 independent variables and 16 observations produced the following results: SSE = 15 and R2= 2/3.Complete the analysis of variance table and calculate the F statistic.

At α\alphaα = .05 test to determine if at least one of the two new independent variables make a significant contribution to the multiple regression model.

A multiple regression model with 3 independent variables and 16 observations produced the following analysis of variance table.

A multiple regression model with four independent variables consists of 29 observations.The multiple coefficient of determination is R²= .80 and the standard error is s = 2.0.Complete the analysis of variance table for this model and test the overall model for significance.

A multiple regression model with 3 independent variables and 16 observations produced the following results: SSE = 15 and R²= 2/3.Complete the analysis of variance table and calculate the F statistic.

At $\alpha$ = .05 test to determine if at least one of the two new independent variables make a significant contribution to the multiple regression model.