Exam 12: Multiple Regression and Model Building

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 variable is the amount of time spent in the hospital (in days),the quantitative independent variables include the age of the patient,cholesterol level of the patient,and blood pressure of the patient.Define the dummy variables so that all other hospitals are compared to the City hospital (base).

In a multiple regression a very high correlation between predictors would suggest there is an issue of multicollinearity.

Multicollinearity hinders the regression model's ability to predict the dependent variable on the basis of a combination of values of the independent variable in the experimental region.

The 95% prediction interval for the point estimate given above is from 33.9 to 65.74.Interpret the meaning of this interval.

Test the overall usefulness of the model at alpha = .05.Calculate the F statistic and make your decision.

The multiple coefficient of determination can assume any value between 0 and 1,inclusive.

In multiple regression analysis,the explained variation divided by the total variation yields the:

A member of the provincial legislature has expressed concern about the differences in the mathematics test scores of grade 9 high school students across the province.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 province 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 Predictor Coef SE Coef Constant 35.178 7.595 Math Dgr 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 Math Dgr 1 672.10 Age 1 363.09 Salary 1 17.90 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 Obs Fit Standard Deviation Fit 1 65.12 1.68 -Determine the 95% confidence interval for this estimate and interpret its meaning.

A multiple regression model with 3 independent variables and 16 observations produced the following analysis of variance table.

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

When using a multiple linear regression model,data transformations on the dependent variable may be used in order to correct a violation of a(n)__________ of the multiple regression model.

Which of the following residual plots is not used in regression analysis?

A(n)______________ may represent an incorrectly entered data value and may influence the results of a regression equation.

Determine the 95% interval for β₁(beta coefficient for the advertising variable).

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

In a multiple regression analysis,if the normal plot approximates the shape of a ____________,then it can be concluded that the assumption of normality for the error terms is not significantly violated.

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.State the appropriate null and alternative hypotheses.

An outlier may be an incorrectly entered data value.

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 df SS Regression 3 31.308 Error (residual) 16 9.378 -What is R²?

In a multiple regression model,a point estimate of ?² is called the ________________ error.