Question

Data were collected from a random sample of 220 home sales from a community. Let Price denote the selling price (in $1000), BDR denote the number of bedrooms, Bath denote the number of bathrooms, Hsize denote the size of the house (in square feet), Lsize denote the lot size (in square feet), Age denote the age of the house (in years), and Poor denote a binary variable that is equal to 1 if the condition of the house is reported as “poor.” An estimated regression yields:

Price=???. ? + ?. ?????? + ??. ????? + ?. ???????? + ?. ???????? + ?. ?????? - ??. ?????

(23.9) (2.61) (8.94) (0.011) (0.00048) (0.311) (10.5)

adjusted R squared = 0.72, SER= 41.5

(a) Suppose that a homeowner adds a new bathroom to her house, which increases the size of the house by 100 square feet. What is the expected increase in the value of the house? Show your work.

(b) What is the loss in value if the homeowner lets his house run down so that its condition becomes “poor”? Explain your answer.

(c) Compute ?? for the regression. (Hint: Think about how you can use information from another measure of fit that is provided here.) Show your work.

(d) Is the coefficient on BDR statistically significantly different from zero at the 5% significance level? Show your work.

(e) Typically five-bedroom houses sell for much more than two-bedroom houses. Is this consistent with your answer to (e) and with the regression more generally? Explain your answer.

(f) A homeowner purchases 2000 square feet from an adjacent lot. Construct a 99% confidence interval for the change in the value of her house. Show your work.

(g) Is the coefficient on Age statistically significantly different from zero at the 5% significance level? Show your work.

(h) The F-statistic for omitting BDR and Age from the regression is F=0.08. Are the coefficients on BDR and Age statistically different from zero at the 5% level? Clearly indicate which numbers you are comparing and your final answer.

Answer 1

(a)

The coefficient of Bath is 23.4

So, addition of Bathroom increases the price by 23.4 * $1000 = $23400

The coefficient of Hsize is 0.156

Addition of 100 sq ft of size increases the price by 0.156 * 100 $1000 = $15600

Expected increase in the value of the house = $23400 + $15600 = $39000

(b)

The coefficient of Poor is -48.8

So, loss of  in value for poor condition = 48.8 * 1000 = $48800

(c)

= adjusted R squared = 0.72

?? = 1 - (1 - ) (n - k - 1) / (n -1) where n is number of observations and k is number of predictors

= 1 - (1 - 0.72) (220 - 6 - 1) / (220 - 1)

= 0.7277

(d)

Let be the coefficient of BDR. The appropriate hypothesis are,

H0: = 0

H1: 0

Test Statistic, t = 0.485 / 2.61 = 0.1858

Degree of freedom = n - k - 1 = 220 - 6 - 1 = 213

For two tail test, P-value = 2 * P(t > 0.1858, df = 213) = 0.8528

Since, p-value is greater than 0.05 significance level, we fail to reject null hypothesis H0 and conclude that there is no strong evidence that coefficient on BDR statistically significantly different from zero at the 5% significance level.