SCENARIO 15-2 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. Model 1: where Y Sale price of property in thousands of dollars Size of property in thousands of square feet 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
-Referring to Scenario 15-2, is the overall model statistically adequate at a 0.05 level of significance for predicting sale price (Y)?
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 estimates are equal to 0.
D)Yes, since the significance of the F-value for the test is smaller than 0.05.

Question

SCENARIO 15-2 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. Model 1:  where Y  Sale price of property in thousands of dollars  Size of property in thousands of square feet  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   
-Referring to Scenario 15-2, is the overall model statistically adequate at a 0.05 level of significance for predicting sale price (Y)?
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 estimates are equal to 0. 
D)Yes, since the significance of the F-value for the test is smaller than 0.05.

Quizplus · Accepted Answer

The question asks whether the overall model is statistically adequate for predicting sale price at a 0.05 level of significance. The best way to evaluate this is to check the significance of the F-value for the model, which tests whether any of the independent variables make a significant contribution to the prediction of sale price. In this case, the partial output shows that the F-value is 14.384 and the corresponding p-value is 0.001, which is smaller than the level of significance of 0.05. Therefore, we can reject the null hypothesis that all of the regression coefficients are equal to zero, and conclude that the overall model is statistically adequate for predicting sale price. Option D is the correct answer. Options A, B, and C are incorrect because they do not address the overall significance of the model, but rather focus on individual t tests or other aspects of the model that need not be related to the overall significance. The question asks whether or not the overall model is statistically adequate at a 0.05 level of significance for predicting sale price. This means we need to look at the F-value for the model. In the output, we see that the F-value is 26.85 and the associated p-value is 0.0003, which is smaller than 0.05. Therefore, we can reject the null hypothesis that all the regression coefficients are equal to zero and conclude that the overall model is statistically significant at a 0.05 level of significance for predicting sale price. Choice D is the correct answer.

SCENARIO 15-2 in Hawaii, Condemnation Proceedings Are Under Way to Enable