You are given the following estimated equation: ln(assess) = 4.97 + 0.00037sqrft

Question

You are given the following estimated equation: ln(assess) = 4.97 + 0.00037sqrft - 0.0082bdrms - 0.0585colonial + 0.000047sqrftcol Std. Errors (0.088) (0.000042) (0.0201) (0.1050) (0.00005) n = 88, R-square = 0.7561 Where the variables are described as follows: In(assess) = the natural log of 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 coefficient estimate in this equation. Are the variables sqrft and bdrms individually significant at 5%? Are all the explanatory variables jointly significant at 5%? Calculate the estimated effect of threel additional bedrooms of 150 sqrft each, on the assessed value of a non-colonial house? Of a colonial house?

Explanation / Answer

a) If all the variables are 0 then dependent variable will be 4.97. ie equal with intercept term.

if sqrft changes by 1unit then log of assesed house value will be changed by 0.00037unit if sqrft change in positive side by 1 unit then change in dependent variable will be positive. similarly bdrms,colonial has inverse relation with dependent variable if bdrms increase by 1 unit then ln(assess) will decrease by 0.0082 similarly for colonial it will decrease by 0.0585. For 1unit increase in sqrftcol ln(assess) will change by 0.000047.

b)yes both of them are significant because for both of them 2xstandered error is less than 5.

c)yes all the varables are significant. Because none of them is crossing 5% confidence limit, besides this R square is also good. But in this case sqrftcol must have strong multicollinearity with sqrft and colonial.

D) for colonial house effect is

150x0.00037 -3x0.0082-0.0585

and for non colonial

150x0.00037 -3x0.0082

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