Exam 12: Multiple Regression and Model Building

The range of feasible values for the multiple coefficient of determination is from:

Consider the following partial computer output for a multiple regression model. Predictor Coefficient Standard Deviation Constant 41.225 6.380 1.081 1.353 -18.404 4.547 Analysis of Variance Source Regression 2 2270.11 Error (residual) 26 3585.75 -Test the overall usefulness of the model at ? = .01.Calculate F and make your decision.

In using the multiple regression method,we can model the effects of the different levels of a qualitative independent variable by using a(n):

In a multiple regression analysis,the current model has three independent variables.The analyst decides to add another (fourth)independent variable from the same data set while retaining the other three independent variables.As a result of this addition,the value of MSE will ____________ decrease.

For the same point estimate of the dependent variable and the same level of significance,the confidence interval is always wider than the corresponding prediction interval.

In a multiple regression analysis,the least squares prediction equation is computed as $\hat { y }$ = 84.2 + 6.3x₁ - 9.4x₂.If we hold x₂ constant and increase x₁ by 2 units,what is the estimated change in the mean value of y?

The term _________ refers to the situation in which the relationship between the mean value of the dependent variable and an independent variable is dependent upon the value of another independent variable.

In the interaction model y = β₀+ β₁X₁+ β₂X₂+ β₃X₁X₂+ ε,we would first test the significance of _____.

Dropping an independent variable from a multiple linear regression model will always result in:

The range of the previously observed combinations of values of the independent variables is referred to as the _____.

In a multiple regression analysis,the current model has three independent variables.The analyst decides to add another (fourth)independent variable from the same data set while retaining the other three independent variables.As a result of this addition,the value of explained variation will ____________ decrease.

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's 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. x2and x3are dummy variables,and they are defined below. x2= 1,if weekend x2= 0,otherwise x3= 1,if weather is favourable 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: $\hat { y } = - 1050 + 250 x _ { 1 } + 2200 x _ { 2 } + 5400 x _ { 3 }$ The multiple regression compute output also indicated the following: $s _ { b _ { 1 } } = 800 , s _ { b _ { 2 } } = 1000 , s _ { b _ { 3 } } = 1850$ -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.

A county has four major hospitals: 1)Regional Memorial;2)General;3)Charity;and 4)City.A multiple regression model is used to compare the time spent in the hospital after a heart by-pass surgery among the four hospitals.The response (dependent)variable is the amount of time spent in the hospital (in days).The variables used to predict the time spent in the hospital include the patient's age,cholesterol level (in mlg. ),blood pressure,as well as variables indicating the hospital in which the surgery was performed.Determine the total number of independent variables in the multiple regression model.Indicate how many of these are quantitative variables and how many are indicator (dummy)variables.

In the quadratic regression model,y = $\beta$ ₀ + $\beta$ ₁X + $\beta$ ₂X²+ $\varepsilon$ The ?₂ term represents the:

If the correlation coefficient between two independent variables is greater than .90,then ______________________ is considered to be severe.

The y intercept (?₀)in a multiple regression model represents the estimated value of the ________ variable,when the value of all independent variables are _______.

Given the regression model y = β₀ + β₁X₁ + β₂X₂ + ε,if we are testing the significance of the independent variable X₁ and we reject the null hypothesis H₀: β₁= 0,we conclude that:

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's 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. x2and x3are dummy variables,and they are defined below. x2= 1,if weekend x2= 0,otherwise x3= 1,if weather is favourable 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: $\hat { y } = - 1050 + 250 x _ { 1 } + 2200 x _ { 2 } + 5400 x _ { 3 }$ The multiple regression compute output also indicated the following: $s _ { b _ { 1 } } = 800 , s _ { b _ { 2 } } = 1000 , s _ { b _ { 3 } } = 1850$ -Interpret the estimated model coefficient b3.

Test the usefulness of variable x₁ in the model at α = .05.Calculate the t statistic and state your conclusions.

Below is a partial multiple regression ANOVA table. Source SS df Model 0.242 2 Error 0.105 3 -Calculate the adjusted R².