1. A developer who specializes in summer cottage property is considering purchasing a large tract of land adjoining a lake. The current owner of the tract has already subdivided the land into separate building lots and has prepared the lots by removing some of the trees. The Developer wants to forecast the value of each lot. From previous experience, she knows that the most important factors affecting the price of the lot are size (lot size), number of mature trees (Trees), and distance to the lake (Distance). From a nearby area, she gathers data for 60 recently sold lots. These data are stored in Devloper.xls.
(a) Perform a multiple regression in Excel and provide excel output for the regression model = βo + βo(Lot size) + βo(Trees) + βo(Distance) + ∈
(b) Write down the equation for regression line.
(c) What is the standard error of estimate? Interpret its value.
(d) What is the coefficient of determination? What does this statistic tell you?
(e) What is the coefficient of determination, adjusted for degrees of freedom? Why does this value differ from the coefficient of determination? What does this tell you about the model?
(f) Test the overall utility of the model. What does the p-value of the test statistic tell you?
(g) Interpret each of the coefficients.
(h) Test to determine whether each of the independent variables is linearly related to the price of the lot.
2. The marketing manager for a chain of hardware stores needs more information about the effectiveness of the three types of advertising that the chain uses. These are (i) localised direct mailing (in which flyers describing sales and product features are distributed to homes in the surrounding area), (ii) newspaper advertising and (iii) local television advertising. To determine which type of advertising is most effective, the manager collects one week's data from 100 randomly selected stores. For each store, the following variables are recorded:
Weekly gross sales
Weekly expenditures on direct mailing
Weekly expenditures on newspaper advertising Weekly expenditures on television commercials
All variables are recorded in thousands of dollars and stored in columns 1 to 4, respectively, in file GrossSales.xls.
a. Find and write out the regression line.
b. What is the Coefficient of Determination? What is the Coefficient of Determination adjusted for degrees of freedom? What do these statistics tell you about the regression model? Using the ANOVA table, calculate R2, the Adjusted R2 and the standard error of the estimate, Sε. Confirm that these values are the same as those shown in the computer output.
c. What does the standard error of the estimate tell you about the regression model (compare with the mean weekly gross sales, which you will need to compute)?
d. Test the overall utility of the model using an F-Test. What does the p-value of this test tell you?