Exam 14: Multiple Regression

Below is a partial multiple regression ANOVA table. What is the mean square error?

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 = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\beta$ ₃x₃ + $\varepsilon$ 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 compute 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.

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 S = 5.465 R - Sq = 96.7% R - Sq(adj)= 95.0% Analysis of Variance 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% prediction interval for this point estimate.

Consider the following analysis of variance table from a multiple regression model.Test the model for overall usefulness at = .01 and carefully make a managerial conclusion.

An acceptable residual plot exhibits:

Below is a partial multiple regression computer output. Test the usefulness of variable x₅ in the model at $\alpha$ = .05.Calculate the t statistic and state your conclusions.

Below is a partial multiple regression ANOVA table. Calculate the adjusted R².

Below is a partial multiple regression ANOVA table. What is the total sum of squares,explained variation,mean square error and the number of observations in the sample?

Below is a partial multiple regression ANOVA table. Calculate the explained variation.

The multiple _________ measures the proportion of the variation in y (response variable)explained by the multiple regression model or the set of independent variables included in the multiple regression equation.

A member of the state legislature has expressed concern about the differences in the mathematics test scores of high school freshmen across the state.She asks her research assistant to conduct a study to investigate what factors could account for the differences.The research assistant looked at a random sample of school districts across the state and used the factors of percentage of mathematics teachers in each district with a degree in mathematics,the average age of mathematics teachers and the average salary of mathematics teachers s = 7.62090 Analysis of Variance Test the usefulness of variable x₁ in the model at $\alpha$ = .05.Calculate the t statistic and state your conclusions.

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 S = 5.465 R - Sq = 96.7% R - Sq(adj)= 95.0% Analysis of Variance 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: $\beta$ ₂ $\le$ 0,at $\alpha$ = 0.05,and state your conclusions.

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

A(n)________ plot is a residual plot that is used for the purpose of checking the normality assumption of the multiple regression model.

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 S = 5.465 R - Sq = 96.7% R - Sq(adj)= 95.0% Analysis of Variance Interpret the regression coefficients for the variables advertising,price and store.

Below is a partial multiple regression computer output. Test the overall usefulness of the model at = .01.Calculate the F statistic and make your decision.

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

A member of the state legislature has expressed concern about the differences in the mathematics test scores of high school freshmen across the state.She asks her research assistant to conduct a study to investigate what factors could account for the differences.The research assistant looked at a random sample of school districts across the state and used the factors of percentage of mathematics teachers in each district with a degree in mathematics,the average age of mathematics teachers and the average salary of mathematics teachers s = 7.62090 Analysis of Variance Based on the multiple regression model given above,estimate the mathematics test score and calculate the value of the residual,if the percentage of teachers with a mathematics degree is 50.0,the average age is 43 and the average salary is 48,300 (48.3).The actual mathematics test score for these factors is 68.50.

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 S = 5.465 R - Sq = 96.7% R - Sq(adj)= 95.0% Analysis of Variance 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% interval for $\beta$ ₁ (beta coefficient for the advertising variable).

Consider the following partial computer output for a multiple regression model. Test the overall usefulness of the model at $\alpha$ = .01.Calculate F and make your decision.