A researcher collects data to study the effect of some house characteristics on

Question

A researcher collects data to study the effect of some house characteristics on the sale price. The data include the following variables • Ip = log of the sale price of the house (in dollars) • 11 = log of the houses lot size (in square feet) • bdrms = the number of bedrooms in the house • fb = the number of full bathrooms in the house • drive = 1 if the house has a driveway 1. (24 points) find the values of T1 – Tg . 2. (5 points) If there is a house with 4000 square feet, 2 bedrooms, 1 full bathroom, and no driveway. What is your best estimate of the sale price? Be careful of the log. 3. (6 points) Can you test whether the number of bedrooms has a significant effect on the sale price? How about the lot size? Be precise.

Explanation / Answer

a) x1 = 2.76 + 6.07 = 8.83

x2 = 113-109 = 4

x3 = 2.76/8.83 = 0.312

x6 = 0.1371928/0.0999759 =1.37

x7 = 0.1371928 - 1.96*0.0999759 = -0.058

x8 =0.1371928 + 1.96*0.0999759= 0.333

now

x4/x5 = 6.26 , coeff/ SE = t value , also coeff +1.96*SE = upper value and coeff - 1.96*SE = lower value

6.26x5 -1.96*x5 = 0.2673005

solve for x5

x5 = 0.2673005/4.3 = 0.06216

so x4 = 0.06216 *6.26 = 0.389

b) The regression equation is sale price = 0.33789*bdrms +0.137*fb + 0.0575*drive +6.672

c) as the p value of the bedroom , from the output table is 0.169 , which is not less than 0.05 . Hence we fail to reject the null hypothesis and conclude that the variable bdrms is not signficant for the model

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