Exam 14: Multiple Regression and Model Building

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.

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.

If we are predicting y when the values of the independent variables are x₀₁,x₀₂,... ,x_0k,the farther the values of x₀₁,x₀₂,... ,x_0k are from the center of the observed data,the smaller the distance value and the more precise the associated confidence and prediction intervals.

For a given multiple regression model with three independent variables,the value of the adjusted multiple coefficient of determination is _________ less than R².

Consider the following partial computer output for a multiple regression model. Determine the 95 percent interval for β₂ and interpret its meaning.

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

A partial F test is used to assess when at least one variable in a subset of squared and interaction variables in the multiple regression model is significant.

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.

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

Below is a partial multiple regression computer output. Write the least squares prediction equation.

In a multiple regression model,we can conclude that multicollinearity exists if the average variance inflation factor is substantially greater than _____.

The graph of the prediction equation obtained from the model is a(n)__________.

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. Additional information related to this point estimate of 65.12 is given below. Predicted Values for New Observations: New Determine the 95 percent confidence interval for this estimate and interpret its meaning.

Plotting the residuals in a time-ordered sequence will reveal possible violations of the __________ of error terms assumption.

Given the regression model y = β₀ + β₁x₁ + β₂x₂ + β₃x₁² + β₄x₂² + ε,if we wish to test the significance of higher-order terms (x₁² and x₂²),we would use the following test.

Multicollinearity is severe if the largest variance inflation factor (VIF)is greater than _____.

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. Determine the 90 percent interval for β₂ and interpret its meaning.

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

The variance inflation factor measures the relationship between the dependent variable and the rest of the independent variables in the 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 Interpret the regression coefficients for the variables Advertising,Price,and Store.