Exam 13: Multiple Regression Analysis

The adjusted value of is used mainly to compare two or more regression models that have the same number of independent predictors to determine which one fits the data better.

In a multiple regression model, adding more independent variables that have a low correlation with the dependent variable will decrease the value of the coefficient of multiple determination.

Electric Usage Narrative The power company claims the amount of electricity used by a house (y) depends on = square metres of heated space, = mean outside temperature, and = mean hours of sunlight per day. Partial statistical software output is given below. Regression Analysis The regression equation is = 357 + 0.808 - 16.6 + 40 S = 267.7 R-sq = 82.0% R-sq(adj) = 76.6% Analysis of Variance -Refer to Electric Usage Narrative. Construct a 99% confidence interval for .

A multiple regression model forms a plane through multidimensional space.

Assume that a company is tracking its advertising expenditures as they relate to television ( ) and radio advertising ( ). The owner of the company believes that it would improve the regression model to add a third variable that represents the sum of the advertising on radio and television ( = + ). This assessment is generally correct.

A coefficient of multiple correlation is a measure of how well an estimated regression plane (or hyperplane) fits the sample data on which it is based.

One of the consequences of multicollinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.

What is stepwise regression, and when is it desirable to make use of this multiple regression technique?

Demographic Variables and TV Narrative A statistician wanted to determine if the demographic variables of age, education, and income influence the number of hours of television watched per week. A random sample of 25 adults was selected to estimate the multiple regression model: , where y is the number of hours of television watched last week, is the age (in years), is the number of years of education, and is income (in $1000s). The computer output is shown below. The regression equation is S = 4.51 R-Sq = 34.8% Analysis of Variance -Refer to Eating Habits of Canadians. Use the prediction equation to find a point estimate of the average beef consumption per family of three in 2005. Compare this value with the value labelled "Fit" in the printout.

Demographic Variables and TV Narrative A statistician wanted to determine if the demographic variables of age, education, and income influence the number of hours of television watched per week. A random sample of 25 adults was selected to estimate the multiple regression model: , where y is the number of hours of television watched last week, is the age (in years), is the number of years of education, and is income (in $1000s). The computer output is shown below. The regression equation is S = 4.51 R-Sq = 34.8% Analysis of Variance -Refer to Demographic Variables and TV Narrative. Is there sufficient evidence at the 1% significance level to indicate that hours of television watched and age are linearly related? Justify your conclusion.

In testing the significance of a multiple regression model in which there are three independent variables, the null hypothesis is .

College Textbook Sales Narrative A publisher of college textbooks conducted a study to relate profit per text y to cost of sales x over a six-year period when its sales force (and sales costs) were growing rapidly. These inflation-adjusted data (in thousands of dollars) were collected: Expecting profit per book to rise and then plateau, the publisher fitted the model to the data. -Refer to College Textbook Sales Narrative. What sign would you expect the actual value of to have? Find the value of in the printout. Does this value confirm your expectation? Justify your answer.