Introductory Econometrics: A Modern Approach 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) 0 1log(nox) 2rooms u. (i) What are the probable signs of 1 and 2? What is the interpretation of 1? 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 1? (iii) Using the data in HPRICE2.RAW, the following equations were estimated: log(price) 11.71 1.043 log(nox), n 506, R2 .264. log(price) 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 an- swer in part? (ii) Does this mean that .718 is definitely closer to the true elasticity than 1.043?