You are given the following equation: assess = 33.58 + 0.134sqrft + 2.575bdrms -

Question

You are given the following equation: assess = 33.58 + 0.134sqrft + 2.575bdrms - 18.475colonial + 0.1137sqrftcol Std. Errors (32.54) (0.0153) (7.723) (38.55) (0.0185) n = 88, R-square = 0.7515 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 Provide an interpretation for each partial slope estimate in this equation. Are the variables sqrft and bdrnis individually significant at 5%? Are all the explanatory variables jointly significant at 5%? Calculate the estimated effect of three 1 additional bedrooms of 150 sqrft each, on the assessed value of a non-colonial house? Of a colonial house?

Explanation / Answer

a. If the number of square feet of the house increases by 1 unit , then the assessed house value will increase by $134, all the other thins remaining constant. If the number of bedrooms in the house increases by 1 unit, then the assessed house value will increase by $2575, all other things remaining constant. It the house is of colonial type, then the value of the house increases by $ 18475, all other things remaining constant. If the house is of colonial type then increase in the size of the house by 1 unit will increase its assessed value by $1.137.

b. At 5 per cent level of significance, the number of bed rooms in the house are statically significant but not the number of square feet.

c. For joint significance, F value is needed which is not given in the question, so I will assess the R value which is around 75 per cent. This states that there are other variables also which can explain the value of the house.

d. Effect on the value of colonial house = 33.58 + 0.134 * 150 * 3 + 2.575 * 3 - 18.475 + 0.1137 * 150 * 3 * 1

   = $ 134.295 thousand

Effect on the value of non colonial house = 33.58 + 0.134 * 450 + 2.575 * 3

   = $101.605 thousand

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