Question

5. 1 Data were collected for a random sample of 220 home sales from a U.S. community in 2003 Let Price denote the selling price (in $1000), BDR the number of bedrooms, Bath the number of bathrooms, Hsize the size of the house (in sq. ft.), Lsize the lot size (in sq. ft.), Age the age of the house (in years), and Poor a binary variable that is equal to 1 if the condition of the house is reported as YpoorY. An estimated regression yields the following output where standard errors are given in brackets Price- 119.2 +0.485BDR+23.4Bath +0.156H size + 0.002 Lsize +0.090 Age -48.8 Poor (0.011) (0.311) (10.5) (23.9) (2.61) (0.00048) (8.94) 0.08; SER-11.5 (a) Interpret the coefficients. (b) Is the coefficient on BDR statistically significantly different from zero? (c) Typically, five-bedroom houses sell for much more than two-bedroom houses. Is this consistent with your answer to (a) and with the regression more generally? Based on Stock/Watson, p.213, 248. (d) A homeowner purchases 2000 square feet from an adjacent lot. Construct a 95% confidence interval for the change in the value of her house (e) The F-statistic for omitting BDR and Age from the regression is F 0.08. Are the coefficients on BDR and Age jointly statistically significant from zero at the 5% level? 10% level?

Answer 1

(a) there is negative impact of variable poor on price and remaining has positive impact on price

(b) BDR is non-significant as its t-value is less than critical value

(c) since the BDR is non-significant ,so it is not consistent with regression model

(f) here the 95% confidence interval for Lsize=0.002$\pm$1.9711*0.00048=0.002000$\pm$0.000946=(0.001154, 0.002946)

required confidence interval=(2000*0.001154, 2000*0.002946)=(2.308, 5.892)

(e) not significant at 5%( as the p-value is more) and significant at 10% ( as the p-value is less)

variable	coeffficient	SE	t=coefficient/SE	critical t(0.05/2,213)	Remarks
BDR	0.485	2.61	0.185823755	1.971164	non-significant
Bath	23.4	8.94	2.617449664	1.971164	significant
H size	0.156	0.011	14.18181818	1.971164	significant
Lsize	0.002	0.00048	4.166666667	1.971164	significant
Age	0.09	0.311	0.289389068	1.971164	non-significant
Poor	-48.8	10.5	-4.647619048	1.971164	significant