Exam 14: Multiple Regression

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

Consider the following partial computer output for a multiple regression model. Analysis of Variance Write the least squares prediction 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 Calculate R².

Consider the following partial computer output for a multiple regression model. Analysis of Variance Determine the 95% interval for $\beta$ ₂ and interpret its meaning

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

In a multiple regression model,the explained sum of squares divided by the total sum of squares yields 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 Additional information related to this point estimate of 65.12 is given below. Predicted Values for New Observations 50% with math degree,average age of 43 and average salary is 48.3 New Determine the 95% confidence interval for this estimate and interpret its meaning.

Regression models that employ more than one independent variable are referred to as multiple regression models.

Consider the following partial computer output for a multiple regression model. Analysis of Variance Calculate the adjusted 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 = $\beta$ 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: Interpret the estimated model coefficient b₃.

Consider the following partial computer output for a multiple regression model. Analysis of Variance Test the usefulness of variable x₂ in the model at = .05.Calculate the t statistic and state your conclusions.

The _____ term describes the effects on y of all factors other than the independent variables in a multiple regression model.

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

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 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.

Below is a partial multiple regression ANOVA table. What is the total sum of squares and the degrees of freedom for total sum of squares?

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 What is the mean square error?

Consider the following partial computer output for a multiple regression model. Analysis of Variance What is the number of observations in the sample?

A t-test is used in testing the significance of an individual independent variable.

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 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.

The effects of different levels of qualitative independent variables are described using _____ variables.