Lesson_12n13_Workbook_F12_Version_Space_

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Unformatted text preview: tic. 3 c. What is the coefficient of determination? What does this statistic tell you? d. Test the validity of the model. e. Interpret each of the coefficients. 4 f. Can Pat infer that the assignment mark is linearly related to the final grade in this model? g. Can Pat infer that the midterm mark is linearly related to the final grade in this model? h. Predict Pat’s final exam mark. PROBLEM # 12.6 The marketing manager for a chain of hardware stores needed more information about the effectiveness of the three types of advertising that the chain used. These are localized direct mailing (in which flyers describing sales and featured products are distributed to homes in the area surrounding a store), newspaper advertising, and local television advertisements. To determine which type is most effective, the manager collected 1 week’s data from 100 randomly selected stores. For each store, the following variables were recorded: • • • • • Weekly gross sales Weekly expenditure on direct mailing Weekly expenditures on newspaper advertising Weekly expenditures on television commercials All variables were recorded in thousands of dollars. 5 a. Find the regression equation. b. What is the coefficient of determination? What do these statistics tell you about the regression equation? c. What does the standard error of estimate tell you about the regression model? d. Test the validity of the model. e. Which independent variables are linearly related to weekly gross sales in this model? Explain. f. Compute the 95% interval of the week’s gross sales if a local store spends $800 on direct mailing, $1,200 on newspaper advertisements, and $ 2,000 on television commercials. (Optional) 6 g. Calculate the 95% interval of the mean weekly gross sales for all stores that spend $800 on direct mailing, $ 1,200 on newspaper advertising, and $2,000 on television commercials. (Optional) h. Discuss the difference between the two intervals found in Parts f and g. PROBLEM # 12.7 What is multicollinearity, and how can it adversely affect multiple regression analysis? How can we tell whether multicollinearity is present? There are several clues to the presence of multicollinearity: (1) an ____________________variable known to be an important_____________________________ _________________________________________________________________________________________________________ _______________________________________. (2) a partial regression coefficient exhibits the _______________________; and/or, (3) when an ________________________________________________________________________________, the partial regression coefficients for the other variables______________________________ ____________________________________________________________________.. ___________________...
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