# ps5_sol - Department of Economics Columbia University...

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Department of Economics W3412 Columbia University Spring 2010 SOLUTIONS TO Problem Set 5 Introduction to Econometrics Prof. Marcelo J. Moreira and Seyhan E Arkonac, PhD for all sections Spring 2010 1. hprice1.dta is a data set collected from the real estate pages of the Boston Globe during 1990. These are homes that sold in the Boston, MA area. Variables are explained in table below. In this problem set you will take a look at some empirical evidence on housing prices of 1990 in Boston, MA area. Note that, to do this problem set, you will need to create (generate) some new variables, which are functions of the variables in hprice1.dta a) Regress lprice on llotsize, lsqft, bdrms and colonial. Interpret the coefficient of (i) llotsize, (ii) lsqft and (iii) bdrms. . reg lprice llotsize lsqrft bdrms colonial,r Linear regression Number of obs = 88 F( 4, 83) = 34.50 Prob > F = 0.0000 R-squared = 0.6491 Root MSE = .18412 ------------------------------------------------------------------------------ | Robust lprice | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- llotsize | .1678189 .0440356 3.81 0.000 .0802338 .2554041 lsqrft | .7071931 .1090447 6.49 0.000 .4903076 .9240787 bdrms | .0268305 .032718 0.82 0.415 -.0382444 .0919053 colonial | .0537962 .0489041 1.10 0.274 -.0434721 .1510645 _cons | -1.349589 .8115795 -1.66 0.100 -2.963788 .2646099 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ (i) 10% increase in lot size will cause price to increase by 1.6% keeping other variables constant. (Elasticity of price with respect to lot size is 0.17) (ii) 10% increase in the size of the house will cause price to increase by 7% keeping other variables constant. (Elasticity of price with respect to the size of the house is 0.7) (iii) An additional bedroom will increase the price of the house by 2.68% keeping other variables constant.

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b) Now regress lprice on llotsize, llotsize 2 , lsqft, lsqft 2 , bdrms and colonial. Note it is now difficult to interpret the coefficient of (i) llotsize and (ii) lsqft due to the nonlinear specification. . reg lprice llotsize llotsize2 lsqrft lsqrft2 bdrms colonial,r Linear regression Number of obs = 88 F( 6, 81) = 27.46 Prob > F = 0.0000 R-squared = 0.6756 Root MSE = .17919 ------------------------------------------------------------------------------ | Robust lprice | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- llotsize | .049371 .4969611 0.10 0.921 -.9394256 1.038168 llotsize2 | .0053273 .0269443 0.20 0.844 -.0482834 .0589381 lsqrft | -8.4956 3.052306 -2.78 0.007 -14.56873 -2.422469 lsqrft2 | .6025779 .2002404 3.01 0.003 .2041623 1.000994 bdrms | .0104218 .0323804 0.32 0.748 -.0540051 .0748486 colonial | .0911863 .0481 1.90 0.062 -.0045176 .1868901 _cons | 34.40863 12.08688 2.85 0.006 10.35953 58.45772 ------------------------------------------------------------------------------ It is hard to interpret the coefficient on X when there is X squared in the regression, because one can not keep X squared constant to interpret X; one can however find the optimum values which minimizes the squared errors. c) Compare the model specification in part (a) to the one in part (b) Both of these regressions have problems insignificant variables in (a) are bdrms and colonial in part (b) llotsize, llotsize 2 are also insignificant. Overall fit measures are better in part (b) but nevertheless, it seems there would be a better model specification. d) Regress price on lotsize, sqrft, bdrms and bdrms 2 . Is there an optimum number of bedrooms that maximizes price of a house? . reg price lotsize sqrft bdrms bdrms2,r Linear regression Number of obs = 88 F( 4, 83) = 16.55 Prob > F = 0.0000 R-squared = 0.6794 Root MSE = 59.544 ------------------------------------------------------------------------------ | Robust price | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- lotsize | .0020749 .0012125 1.71 0.091 -.0003367 .0044866 sqrft | .1221177 .01709 7.15 0.000 .0881265 .1561089 bdrms | -40.2742 48.31517 -0.83 0.407 -136.3711 55.82273 bdrms2 | 6.771337 6.532258 1.04 0.303 -6.221062 19.76374 _cons | 81.67705 91.26611 0.89 0.373 -99.84758 263.2017 ------------------------------------------------------------------------------
Approximately 3 bedrooms minimizes the price of a house. There is no price maximizing value!

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## This note was uploaded on 02/05/2012 for the course ECON W3412 taught by Professor Seyhanarkonac during the Fall '11 term at Columbia College.

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ps5_sol - Department of Economics Columbia University...

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