Exam 12: Multiple Regression and Model Building

In multiple regression analysis an outlier observation is ____________ influential.

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 the adjusted R²will ____________ decrease.

The analyst performing the study wants to determine if at least one of the two new independent variables makes a significant contribution to the multiple regression model.State the appropriate null and alternative hypotheses.

Adding any independent variable to a regression model will always increase:

A multiple regression model with four independent variables consists of 29 observations.The multiple coefficient of determination is R²= .80 and the standard error is s = 2.0.Complete the analysis of variance table for this model and test the overall model for significance.

Below is a partial multiple regression ANOVA table. Source SS df 535.9569 1 1,167.5634 1 18.9886 1 Error 3,459.6803 8 -What is the mean square error?

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 -Calculate the adjusted R².

If we increase the number of independent variables in a multiple regression model,the F statistic will always increase.

In a multiple regression model,as a result of adding a new independent variable,as s ___________,the length of the prediction interval for y will _________.

Below is a partial multiple regression ANOVA table. Source SS df 535.9569 1 1,167.5634 1 18.9886 1 Error 3,459.6803 8 -What is the total sum of squares (total variation)and total degrees of freedom?

If we wish to be 95% confident that we have captured an individual value of the dependent variable for some point in the experimental region,then we should compute a _____.

Below is a partial multiple regression computer output. Source SS df Model 32,774 5 Error 21,886 292 Total 54,660 297 -What is the value of the mean squared error?

Consider the following partial computer output for a multiple regression model. Predictor Coefficient Standard Dev Constant 99.3883 1 -0.007207 0.0031 2 0.0011336 0.00122 3 0.9324 0.373 Analysis of Variance Source 31.308 Regression 3 9.378 Error (residual) 16 -What is the total sum of squares (total variation)?

In a multiple regression model,the explained sum of squares divided by the total sum of squares yields the ___________.

The error term in the regression model describes the effects of all factors other than the independent variables on y (response variable).

Below is a partial multiple regression computer output based on a quadratic regression model. Source SS df Model 29.44 2 Error 59.96 15 Standard Error Variable Coefficient Intercept 8.01 1.45 -1.35 0.55 0.46 0.43 -Determine the number of observations in the sample,explained variation and the MSE.

A researcher in human resources has expressed concern about the differences in job satisfaction results across units within an organization. The researcher conducts a study to investigate what factors could account for the differences. The researcher looked at a random sample of units across the organization and used the factors of percentage of employees with a university degree, the average age of the employees, and the average salary of employees within a unit. The results of the study are presented below: Predictor Coef SE Coef Constant 35.178 7.595 Degree 0.22073 0.07131 Age 0.3353 0.1901 Salary 0.0930 0.1675 $s = 7.62090$ Analysis of Variance Source DF SS Regression 3 1053.09 Residual Error 32 1858.50 Source DF Seq SS Degree 1 672.10 Age 1 363.09 Salary 1 17.90 -Using the results above,what is the total sum of squares?

A researcher in human resources has expressed concern about the differences in job satisfaction results across units within an organization. The researcher conducts a study to investigate what factors could account for the differences. The researcher looked at a random sample of units across the organization and used the factors of percentage of employees with a university degree, the average age of the employees, and the average salary of employees within a unit. The results of the study are presented below: Predictor Coef SE Coef Constant 35.178 7.595 Degree 0.22073 0.07131 Age 0.3353 0.1901 Salary 0.0930 0.1675 $s = 7.62090$ Analysis of Variance Source DF SS Regression 3 1053.09 Residual Error 32 1858.50 Source DF Seq SS Degree 1 672.10 Age 1 363.09 Salary 1 17.90 -Using the results above,the F statistic would be _____.

The model y = β₀ + β₁x₁ + β₂x₂ + β₃x₁x₂ + ε is a __________.

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 b2.