Use the data in KIELMC, only for the year $1981,$ to answer the following questions. The data are for

houses that sold during 1981 in North Andover, Massachusetts 1981 was the year construction began on a local garbage incinerator.

(i) To study the effects of the incinerator location on housing price, consider the simple regression

model

log $(price)=\beta_{0}+\beta_{1} \log (d i s t)+u$

where price is housing price in dollars and dist is distance from the house to the incinerator measured in feet. Interpreting this equation causally, what sign do you expect for $\beta_{1}$ if the presence of the incinerator depresses housing prices? Estimate this equation and interpret the results.

(ii) To the simple regression model in part (i), add the variables log( (intst), log(area), log(land), rooms, baths, and age, where intst is distance from the home to the interstate, area is square footage of the house, land is the lot size in square feet, rooms is total number of rooms, bath is number of bathrooms, and age is age of the house in years. Now, what do you conclude about the effects of the incinerator? Explain why (i) and (ii) give conflicting results.

(iii) Add [log( intst) $]^{2}$ to the model from part (ii). Now what happens? What do you conclude about the importance of functional form?

(iv) Is the square of log(dist) significant when you add it to the model from part (iii)?