Exam 14: Multiple Regression and Model Building

Below is a partial multiple regression ANOVA table. Test the overall usefulness of the model at α = .05.Calculate the F statistic and make your decision.

Consider the following partial computer output for a multiple regression model. What is the adjusted R²?

Below is a partially completed multiple regression analysis of variance (ANOVA)table. Calculate R².

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.

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 An interaction between Advertising and Price is created and the regression analysis is run with the following results: Determine the effect the interaction variable has on sales.

Below is a partial multiple regression computer output based on a quadratic regression model. Test the overall usefulness of the model at α = .05.Calculate the F statistic and make your decision.

Stepwise regression uses a series of ___________ tests during each iteration in order to determine which independent variables should be brought into the regression model.

In contrast to stepwise regression,backward elimination is an iterative model selection procedure that begins with all potential independent variables and then attempts to remove them one at a time based on the p-value of the independent variable.

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

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

A particular multiple regression model has 3 independent variables,the sum of the squared error is 7680,and the total number of observations is 34.What is the value of the standard error of estimate?

Calculate the odds ratio for an event when its probability is 0.75.

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 looks at a random sample of school districts across the state and uses 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. Test the usefulness of variable x₁ in the model at α = .05.Calculate the t statistic and state your conclusions.

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.

The general form of the quadratic multiple regression models is:

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

In comparing regression models,the regression model with the largest R² will also have the smallest standard error (s).

Below is a partial multiple regression computer output. Determine the number of observations in the sample,the number of independent variables in the model,and the mean squared error.

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

Dummy variables take on the values of _________ and are used to model the effects of different levels of qualitative variables.