solution

The housing business suspected that the effect of number of bedrooms on price might not be linear and that some of the independent variables might interact to affect the price. Hence, the businesses added the following variables to Model 1: bdrms², sqrft*bdrms, and lotsize*colonial.

The Excel output for this new Model 2 was provided below.

Model 2:

??????????=??0+??1??????????????+??2??????????+??3??????????+??4????????????????+??5??????????2+??6??????????*??????????+??7??????????????*????????????????+??price=ß0+ß1lotsize+ß2sqrft+ß3bdrms+ß4colonial+ß5bdrms2+ß6sqrft*bdrms+ß7lotsize*colonial+e

ANOVA
	df	SS	MS	F
Regression	7
Residual		263968
Total	87	917855
	Coefficients	Standard Error	t Stat	P-value
Intercept	131.772	96.002	1.373	0.174
lotsize	0.005	0.002	2.936	0.004
sqrft	0.028	0.051	0.554	0.581
bdrms	-31.696	41.501	-0.764	0.447
colonial	52.611	21.828	2.410	0.018
bdrms^2	-0.737	6.280	-0.117	0.907
sqrft*bdrms	0.022	0.012
lotsize*colonial	-0.004	0.002	-1.962	0.053

Use Model 2 to answer parts f – i.

f. Predict the average price (in dollars) for a house of colonial style with 9000-square-foot lot size, 2000-square-foot house size, and 3 bedrooms.

g. Estimate the change in average price (in dollars) for houses with three bedrooms for every square foot increase in house size, holding all other independent variables constant.

h – (i). Conduct an F test to determine whether bdrms², sqrft*bdrms, and lotsize*colonial contribute significantly to the model. Use ??a = 0.05. Compute the test statistic value.

h – (ii). What is the p-value?

Group of answer choices

p-value is less than 0.01

p-value is between 0.05 to 0.1

p-value is between 0.025 to 0.05

p-value is between 0.01 to 0.025

h – (iii). Find the critical value.

h – (iv). What is your conclusion?

Group of answer choices

Reject H₀. At least one of these variables is significant.

Reject H₀. None of these variables is significant.

Do not reject H₀. None of these variables is significant.

Do not reject H₀. At least one of these variables is significant.

i – (i). Construct a confidence interval to determine whether the number of bedrooms and house size interact to affect the price. Use 0.05 level of significance.

Group of answer choices

-114.283 to 50.891

-0.002 to 0.046

-0.004 to 0.053

-0.073 to 0.129

i – (ii). What is your conclusion?

Group of answer choices

Since the confidence interval contains 0, the number of bedrooms and house size don’t interact to affect the price.

Since the confidence interval contains 0.022, the number of bedrooms and house size interact to affect the price.

Since the confidence interval contains 0.022, the number of bedrooms and house size don’t interact to affect the price.

Since the confidence interval contains 0, the number of bedrooms and house size interact to affect the price.