Homework 3 100 points The following two problems will require a lot of calculations in STATA or however you opt to execute the calculations It will generate many pages of output Here is how your should organize it The first pages should contain your answers to all the questions along with showing any key algebraic equations or explanations you need to use along the way After that include a printout of the output from the regressions you executed in support of your answers Highlight any numbers in this output that you used in the first section To save paper you may print this section double side and or with 2 up format Last include a copy of the DO file that contains the commands you asked STATA to execute Be sure you organize these in a way that will be clear to the reader 1 With this assignment you will find a STATA data file called HW3 Housing dta For reference the variables in this file are price House Price in sqft Total square feet of living area beds Number of bedrooms baths Number of full bathrooms age age of house in years stories number of stories of the house vacant If yes this variable 1 If no this variable 0 Open this dataset within STATA Before you begin answering the following it s not a bad idea to ask STATA to summarize the data using the command summarize You should also start a log file to store your results 52 points total 12 parts worth 4 each 4 points free a Run the following regression See Output b Hypothesize the sign of the bias if any resulting from excluding sqft from the regression Explain your reasoning The bias is likely to be positive Higher square feet holding beds constant will likely raise prices Number of bedrooms and sqft are also likely to be positively related The product of these two is positive c Use the data to verify or not your claim from b Break down the bias into the component pieces as we did in class The coefficient on beds drops from 32104 to 16217 once we include sqft This suggests the bias was indeed positive exluding age led to an overestimate of the effect of beds of 48321 We have shown in class that omitted variable bias equals the term 2 21 The first element is the coefficient for the omitted variable when it is added to the original regression The second element is the coefficient of a shadow regression of the omitted variable on the original variable In this case when you include the sqft 2 is 95 29 In the shadow regression of sqft on beds the coefficient on beds is 21 507 11 The product of these two is the bias 48321 which confirms our original result d In c you should have noticed that the overall effect of beds is negative once we control for sqft of the house Why is that This makes some sense holding sqft constant more bedrooms can actually be a bad thing Think about it If you have a 2000 square foot house would that house be more valuable with 3 nice sized bedrooms or 10 tiny bedrooms The reason bedrooms was positive originally is that more bedrooms go with bigger houses Once we control for the overall size the number of bedrooms is negatively related to price e Now run the regression See output f At a level of 05 for which if any values of i would you reject the null hypothesis that i 0 Only Baths is not significant with its p value of 62 g What is the predicted price with beds 4 sqft 2185 age 45 baths 2 5 stories 3 Note these are the figures for my house here in State College but the data is not so the price here is pretty meaningless as a predictor of my own home value See output The predicted price is about 135815 82 h According to this model how much will my house change in value five years from today 5 299 07 1495 35 i What percentage of the variation in price is explained by the five X variables The r2 is 71 so 71 of the variation explained by the model Now change the measurement of price Use the gen command gen price thous price 1000 and then use this in place of price in the regression command for part e j Compare the coefficients standard error and t ratio for the independent variables Briefly interpret the difference between this model and the version from part e All the coefficients and standard errors have been reduced by a factor of 1000 The t statistics are unchanged since both the numerator and denominator of the t statistics have also been reduced by a factor of 1000 If you look at the formula for the slope coefficient standard deviation in a single variable regression you can see that reducing the value of Y by a factor of 1000 will lead to both of these terms decreasing by the same factor k Create a new age variable by converting it from years to days 365 days in a year Rerun the regression from e with the new age variable in place of the original age See Output l What has changed between the regression in e and regression in k Be precise The only difference is on the new age days variable Both the coefficient and the standard error have been reduced by a factor of 365 Once again the single variable regression formulas give a clue as to what is going on when you make a transformation of this type to an X variable 2 For the following problem use the STATA dataset called crime dta This data set was compiled by Christopher Cornwell and William Trumbull to study factors that influence crime rates The data set contains observations for 90 counties in North Carolina for 1981 The definitions of the variables are given in the data set According to the economic model of crime rates lower crime rates are associated with better labor markets higher wages more police presence and tougher sentences and lower population density We will use this data set to examine these hypotheses Use a significance level of 05 for all hypothesis tests All of the following regressions will utilize the following subset of variables from this dataset crmrte crime rate prbarr probability of arrest prbconv probability of conviction prbpris probability of a prison sentence avgsen average sentence in days polpc number of police per capita density population density pctmin percent minority taxpc tax revenue per capita wmfg average weekly wage in manufacturing wcon average weekly wage in construction wtuc average weekly wage in transportation utilities and communications wtrd average weekly wage in wholesale and retail trade wfir average weekly wage in finance insurance and real estate wser average weekly wage in services wfed average weekly wage in federal government wsta average weekly wage in state government wloc average weekly wage