In Hawaii, condemnation proceedings are under way to enable private citizens to

Question

In Hawaii, condemnation proceedings are under way to enable private citizens to own the property that their homes are built on. Until recently, only estates were permitted to own land, and homeowners leased the land from the estate. In order to comply with the new law, a large Hawaiian estate wants to use regression analysis to estimate the fair market value of the land. The following model was fit to data collected for n = 20 properties, 10 of which are located near a cove. where Y = Sale price of property in thousands of dollars X1 = Size of property in thousands of square feet X2 = 1 if property located near cove, 0 if not Using the data collected for the 20 properties, the following partial output obtained from Microsoft Excel is shown:

SUMMARY OUTPUT Regression Statistics Multiple R 0.985 R Square 0.970 Standard Error 9.5 Observations 20

ANOVA df SS MS F Signif F Regression 5 28324 5664 62.2 0.0001 Residual 14 1279 91 Total 19 29063

Coeff StdError t Stat P-value Intercept - 32.1 35.7 – 0.90 0.3834 Size 12.2 5.9 2.05 0.0594 Cove – 104.3 53.5 – 1.95 0.0715 Size*Cove 17.0 8.5 1.99 0.0661 SizeSq – 0.3 0.2 – 1.28 0.2204 SizeSq*Cove – 0.3 0.3 – 1.13 0.2749

Referring to Table 15-3, is the overall model statistically adequate at a 0.05 level of significance for predicting sale price (Y)?

Question 1 options: A. No, since some of the t tests for the individual variables are not significant.

B. No, since the standard deviation of the model is fairly large.

C. Yes, since none of the beta-estimates are equal to 0.

D. Yes, since the p-value for the F-test is smaller than 0.05.

Explanation / Answer

Option D is correct.

In general, an F-test in regression compares the fits of different linear models. Unlike t-tests that can assess only one regression coefficient at a time, the F-test can assess multiple coefficients simultaneously. The F-test of the overall significance is a specific form of the F-test. It compares a model with no predictors to the model that you specify.

(Here, the p-value of the F test is 0.0001 which is smaller than 0.05 = level of significance.)

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