Refer to Commercial properties Problems 6.18 and 7.7. Calculate  

 Explain what each coefficient measures and interpret your results. How is the degree of marginal linear association between Y and X₁ affected, when adjusted for X₄?

Problems 7.7

Refer to Commercial properties Problem 6.18.

a Obtain the analysis of variance table that decomposes the regression sum of squares into extra sums of squares associated with X₄; with X₁ given X₄; with X₂ , given X₁ and X₄; and with X₃ , given X₁ X₂ and X₄.

b. Test whether X₃ can be dropped from the regression model given that X_I, X₂ and X₄ a retained. Use the F* test statistic and level of significance .01. State the alternatives, decision rule, and conclusion. What is the P-value of the test?

Problem 6.18

Commercial properties. A commercial real estate company evaluates vacancy rates, square footage, rental rates, and operating expenses for commercial properties in a large metropolitan area in order to provide clients with quantitative information upon which to make rental decisions. The data below are taken from 81 suburban commercial properties that are the newest, best located, most attractive, and expensive for five specific geographic areas. Shown here are the age (X_I), operating expenses and taxes (X_l),vacancy rates (X₃), total square footage (X₄),

a. Prepare a stem-and-leaf plot for each predictor variable. What information do these plots provide?

b. Obtain the scatter plot matrix and the correlation matrix. Interpret these and state your principal findings.

c. Fit regression model (6.5) for four predictor variables to the data. State the estimated regression function.

d. Obtain the residuals and prepare a box plot of the residuals. Does the distribution appear to be fairly symmetrical?

e. Plot the residuals against , each predictor variable, and each two-factor interaction tenn on separate graphs. Also prepare a normal probability plot. Analyze your plots and summarize  your findings.

f. Can you conduct a formal test for lack of fit here?

g. Divide the 81 cases into two groups. placing the 40 cases with the smallest fitted values  into group I and the remaining cases into group 2. Conduct the Brown-Forsythe test for constancy of the error variance, using ex = .05. State the decision rule and conclusion.