The following multiple linear regression equation describes housing prices (variable price, in dollars) in Michigan in terms of the distance (in miles) of the house to an employment center (variable dist), and the nitrogen oxide content (in 100's of grams) in the air (variable nox). The nitrogen oxide content acts as a measure of the harmful pollution that alters the ozone layer in the air surrounding the house. price=a+adist+nox+e When the regression is estimated in STATA, we get the following output. Denote the estimated parameters as: .reg price dist nox Source SS df MS Number of obs = 506 F( 2, 503)= 61.61 Model Residual Total 8.4270e+09 3.4399e+10 4.2826e+10 505 2 4.2135e+09 503 68386774.4 Prob > F = 0.0000 84803032 R-squared Root MSE = 0.1968 Adj R-squared = 0.1936 = 8269.6 price Coef. Std. Err. t P>|t| [95% Conf. Interval] dist -847.0932 273.9594 -3.09 0.002 nox _cons -4573.105 498.0993 -9.18 0.000 51106.61 3645.03 14.02 0.000 -1385.339 -308.8477 -5551.717 43945.25 -3594.494 58267.96 a.) How would the results from this model change if nitrogen oxide is measured in grams. Be sure to specify what happens to all the regression coefficients and R. b.) Suppose that theory predicts that the price of a house depends on the square footage of the house. Under what condition(s) would not including square footage as a regressor not result in biased estimates of the effect of dist and nox on house price. c.) Return to the original model (i.e. nox measured in 100's of grams). Refer to this model as the multiple linear regression. Suppose you want to estimate the simple linear regression: price=8+8dist+u What is the relationship between the estimated effect of distance on price that you would obtain from the simple linear regression and multiple linear regression? The output below is obtained from the regression of nox on dist. Using this information, calculate the coefficient estimate on dist from the simple linear regression. reg nox dist Source Model Residual SS df MS Number of obs = 506 F( 1, 504) = 735.07 402.010323 275.638748 1 402.010323 504 .546902279 Prob > F 0.0000 R-squared 0.5932 Adj R-squared 0.5924 Total 677.649071 505 1.34187935 Root MSE .73953 nox dist _ cons Coef. Std. Err. -.4236297 .0156251 -27.11 0.000 7.157775 .0678114 105.55 0.000 t P>|t| [95% Conf. Interval] -.454328 -.3929314 7.024548 7.291003