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) 5 b0 1 b1log(nox) 1 b2rooms 1 u.

(i) What are the probable signs of b1 and b2? What is the interpretation of b1? 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 up- ward or a downward biased estimator of b1?
(iii) Using the data in HPRICE2.RAW, the following equations were estimated:

log(price) 5 11.71 2 1.043 log(nox), n 5 506, R2 5 .264.
log(price) 5 9.23 2 .718 log(nox) 1 .306 rooms, n 5 506, R2 5 .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 an- swer in part? (ii) Does this mean that 2.718 is definitely closer to the true elasticity than 21.043?