You are given the following estimated equation: assess = 33.58 + 0.134 sqrft + 2

Question

You are given the following estimated equation: assess = 33.58 + 0.134 sqrft + 2.575bdrms - 18.475 colonial + 0.1137 sqrftcol Where the variables are described as follows: assess = the assessed house's value, in $1000 sqrft = the size of the house, in squared feet bdrms = the number of bedrooms in the house colonial = 1 if the house is of colonial style, and 0 if not. sqrftcol = interaction variable equal to sqrft* colonial a. Provide an interpretation for each partial slope estimate in this equation. b. Are the variables sqrft and bdrms individually significant at 5%? c. Are all the explanatory variables jointly significant at 5%? d. Calculate the estimated effect of three additional bedrooms of 150 sqrft each, on the assessed value of a non-colonial house? Of a colonial house?

Explanation / Answer

Answer:

a).

when one square feet of the house increases, house values increases by 0.134(in 1000$).

when one bed room of the house increases, house values increases by 2.575(in 1000$).

when house is colonial, house values decreases by 18.475(in 1000$).

b).

test for sqrft, t =0.134/0.0153 =8.758

calculated t=5.758> t critical at 83 df 1.989. square feet of the house is significant.

test for bdrms, t =2.575/7.723 =0.3334

calculated t=0.3334 < t critical at 83 df 1.989. Number of bed rooms of the house is significant.

c).

F =(0.7515/4)/((1-0.7515)/83)

=62.75101

Calculated F=62.75 > Critical F(4,83) at 5% level 2.482.

The model is significant.

d).

assess=33.58+0.134*sqrft+2.575*bdrms-18.475*colonial+0.1137*sqrftcol

for non colonial,

predicted assess=33.58+0.134*150+2.575*3-18.475*0+0.1137*0

=61.405(in $1000).

for colonial,

predicted assess=33.58+0.134*150+2.575*3-18.475*1+0.1137*150

=59.985(in $1000).

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