Question

ou have collected data on 1,037 residences in North Carolina to analyze the most important determinant of home value. You believe the chief determinants are size and location. To test this, you run the following regression (t-statistics of coefficients in parentheses):

HomeVal = 90.2   +  61.1 Bedrm - 67.8 CrimeBad          R²=0.051

(-3.17). (1.90). (-7.63)

where HomeVal is the value of a home in thousands of dollars, Bedrm is the number of bedrooms in the home, and CrimeBad is equal to 1 if the home is located in a neighborhood in the top 10 percentile of crime in that city, equal to 0 otherwise (that is, located in a safer neighborhood--in the bottom 90 percentile of crime).

a) Interpret the coefficients in a format similar to this answer:

B0 format: If the worker did not have a Bachelor’s degree and was age zero, then the predicted average yearly salary is -2,55 in thousands of dollars. This does not have any economic meaning since workers cannot have age zero! (Even better would be: “the predicted average yearly salary is -$2,554.”) (Note: if you interpreted age to make it age past 5 years of high school graduation that seems a leap from what I wrote, but I let it go.) 2. This is significant at the 95% level because the p-value of 0.02 < 0.05. (Or, “This is significant at the 95% level because the t-stat of |2.34| > 1.96.)

B1 format: If the worker had a Bachelor’s degree, the average yearly salary is predicted to be $7,576 higher than a worker without a Bachelor’s degree, all other variables held constant. (Note: “all other variables held constant” does NOT mean all other variables are zero. Constant means unchanged. Zero means =0! Here, this means something like, “This is what we would predict if we only changed a worker’s degree status but kept their age the same.”) 2. This is significant at the 95% level because the t-stat of t= (7.56/.21) = 36 > 1.96

B2 format: If the worker’s age increases by one year, we would expect the predicted average yearly salary to increase by $605, all other variables held constant. 2. This is significant at the 95% level because 0 does not fall in the 95% confidence interval of [.532, .677]. (Note, check 0 in the CI, not B2. B2 is always in the CI, it’s the center point.)

Thanks!

Answer 1

The average price of a house is 90.2 thousands of dollars

The price value of the house will reduce 67.8 thousands of dollars if the property is in a crime locality

If the property is not in a crime locality, there is no change in the price

Addition of a bedroom will add the price value in 61.1 thousands of dollars

Since the R2 is 0.051, The model can explain only 5% of the variation in the data, hence we can conclude that it is not a good model to explain the value of a home