The following equation describes the median housing price in a community in terms of amoun...

The following equation describes the median housing price in a community in terms of amount of pollution (nox for nitrous oxide) and the average number of rooms in houses in the community (rooms):

log(price) =β0+β1log(nox) +β2rooms + u.

(i) What are the probable signs of β1 and β2? What is the interpretation of β1? Explain.

(ii) Why might nox [or more precisely, log(nox)] and rooms be negatively correlated? If this is the case, does the simple regression of log(price) on log(nox) produce an upward or a downward biased estimator of β1?

(iii) Using the data in HPRICE2.RAW, the following equations were estimated:

= 11.71 - 1.043 log(nox), n = 506, R2 = .264.

= 9.23 - .718 log(nox) + .306 rooms, n = 506, R2 = .514.

Is the relationship between the simple and multiple regression estimates of the elasticity of price with respect to nox what you would have predicted, given your answer in part (ii)? Does this mean that -.718 is definitely closer to the true elasticity than -1.043?