Instruction 16-5
In Hawaii, condemnation proceedings are under way to enable private citizens to own the property upon which their homes are built. 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: Y = β 0 + β 1 X 1 + β 2 X 2 + β 3 X 1 X 2 + β 4 + β 5 X 2 + ε
where
Y = Sale price of property in thousands of dollars
X1 = Size of property in thousands of square metres
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:
Note: Std. Error = Standard Error
-Referring to Instruction 16-5,is the overall model statistically adequate at a 0.05 level of significance for predicting sale price (Y)?
A) Yes, since the p-value for the test is smaller than 0.05.
B) No, since some of the t tests for the individual variables are not significant.
C) No, since the standard deviation of the model is fairly large.
D) Yes, since none of the β-estimates are equal to 0.

Question

Instruction 16-5
In Hawaii, condemnation proceedings are under way to enable private citizens to own the property upon which their homes are built. 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: Y = β 0 + β 1 X 1 + β 2 X 2 + β 3 X 1 X 2 + β 4 + β 5 X 2 + ε
where
Y = Sale price of property in thousands of dollars
X1 = Size of property in thousands of square metres
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:
  Note: Std. Error = Standard Error
-Referring to Instruction 16-5,is the overall model statistically adequate at a 0.05 level of significance for predicting sale price (Y)?
A) Yes, since the p-value for the test is smaller than 0.05. 
B) No, since some of the t tests for the individual variables are not significant. 
C) No, since the standard deviation of the model is fairly large. 
D) Yes, since none of the β-estimates are equal to 0.

Quizplus · Accepted Answer

The overall model is statistically adequate at a 0.05 level of significance for predicting sale price (Y) since the p-value for the test (0.00049) is smaller than 0.05. The null hypothesis for the test is that all β-estimates are equal to 0, and since the p-value is less than the significance level, we reject the null hypothesis and conclude that at least one β-estimate is significantly different from 0, indicating that the model is useful for predicting sale price.

Instruction 16-5 In Hawaii, Condemnation Proceedings Are Under Way to Enable Private