Question 1

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: The multiple regression computer output also indicated the following: Assume today is Saturday morning,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.

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Question 2

Consider the following partial computer output for a multiple regression model. Calculate R².

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Question 3

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: The multiple regression computer output also indicated the following: Interpret the estimated model coefficient b₁.

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Question 4

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:  The sales are in thousands of units per month,the advertising is given in hundreds of dollars per month,and the price is the unit retail price for the particular month.Using MINITAB,the following computer output is obtained.
The regression equation is
Sales = 31.0 + 0.820 Advertising - 0.325 Price + 1.84 Stores    Based on the multiple regression model given above,estimate the monthly light fixture sales and calculate the value of the residual,if the company spends $4000 on advertising,the price of the fixture is $60,and the fixture is being sold at 3 retail stores.

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Question 5

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: The multiple regression computer output also indicated the following: 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.

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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 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: The multiple regression computer output also indicated the following: Interpret the estimated model coefficient b₃.

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Question 7

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

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Question 8

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: The sales are in thousands of units per month,the advertising is given in hundreds of dollars per month,and the price is the unit retail price for the particular month.Using MINITAB,the following computer output is obtained. The regression equation is Sales = 31.0 + 0.820 Advertising - 0.325 Price + 1.84 Stores 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. Determine the 95 percent interval for β₁ (beta coefficient for the advertising variable)and interpret the meaning of the interval.

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Question 9

Below is a partial multiple regression computer output. Determine the 95 percent interval for β₄ and interpret its meaning.

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Question 10

Consider the following partial computer output for a multiple regression model.  What is the mean square error?

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Question 11

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.

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Question 12

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:  The sales are in thousands of units per month,the advertising is given in hundreds of dollars per month,and the price is the unit retail price for the particular month.Using MINITAB,the following computer output is obtained.
The regression equation is
Sales = 31.0 + 0.820 Advertising - 0.325 Price + 1.84 Stores    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.  Determine the 95 percent confidence interval for this point estimate and interpret its meaning.

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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 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: The multiple regression computer output also indicated the following: Assume that the overall model is useful in predicting game attendance.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.

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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 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: The multiple regression computer output also indicated the following: Interpret the estimated model coefficient b₂.

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Question 15

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: The sales are in thousands of units per month,the advertising is given in hundreds of dollars per month,and the price is the unit retail price for the particular month.Using MINITAB,the following computer output is obtained. The regression equation is Sales = 31.0 + 0.820 Advertising - 0.325 Price + 1.84 Stores 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. Test the usefulness of variable Price in the model,using the null hypothesis H₀: β₂ ≤ 0,at α = 0.05,and state your conclusions.

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Question 16

Consider the following partial computer output for a multiple regression model.  What is the total sum of squares?

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Question 17

Consider the following partial computer output for a multiple regression model.  What is the explained variation?

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Question 18

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:  The sales are in thousands of units per month,the advertising is given in hundreds of dollars per month,and the price is the unit retail price for the particular month.Using MINITAB,the following computer output is obtained.
The regression equation is
Sales = 31.0 + 0.820 Advertising - 0.325 Price + 1.84 Stores    Interpret the regression coefficients for the variables Advertising,Price,and Store.

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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 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: The multiple regression computer output also indicated the following: Assume that the overall model is useful in predicting the game attendance.The team statistician wants to know if the mean attendance is higher on the weekends as compared to the weekdays.At α = .05,test to determine if the attendance is higher at weekend home games.

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Question 20

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:  The sales are in thousands of units per month,the advertising is given in hundreds of dollars per month,and the price is the unit retail price for the particular month.Using MINITAB,the following computer output is obtained.
The regression equation is
Sales = 31.0 + 0.820 Advertising - 0.325 Price + 1.84 Stores    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.  Calculate the 95 percent prediction interval for this point estimate and interpret the meaning of this interval.

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Quiz 14: Multiple Regression and Model Building

Consider the following partial computer output for a multiple regression model. Calculate R2.

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

Below is a partial multiple regression computer output. Determine the 95 percent interval for β4 and interpret its meaning.

Consider the following partial computer output for a multiple regression model. What is the mean square error?

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.

Consider the following partial computer output for a multiple regression model. What is the total sum of squares?

Consider the following partial computer output for a multiple regression model. What is the explained variation?

Consider the following partial computer output for a multiple regression model. Calculate R².

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

Below is a partial multiple regression computer output. Determine the 95 percent interval for β₄ and interpret its meaning.

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.