Homework 4 100 points The following two problems will require a lot of calculations in 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 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 YOU ARE ENCOURAGED TO SAVE PAPER BY PRINTING YOUR STATA OUTPUT TWO UP AND DOUBLE SIDED 1 50 points total In this exercise we will study some determinants of housing prices In particular we ll be studying whether being located in same town as a university is important for the price of housing Descriptions of the variables are provided with the dataset utown dta It s always a good idea to make sure you understand what the different variables are before you begin In this case it is also especially important to note the units that the data is provided in a 10 points We ll start with some basic dummy variable regressions to test for differences between groups of houses 1 Regress price on utown Report the coefficients and p values Do homes in university towns have statistically different prices than non universities utown coefficient 61 51 p value 0 000 constant 215 73 0 000 It is not required for credit to give the constant values Yes since the p value on utown is less than any reasonable value of we will reject the null hypothesis that there is no difference between university towns and non university towns In other words there is a statistical difference between the types of towns 2 Regress price on fplace Report the coefficients and p values Do homes with fireplaces have significantly different prices than non fireplaces fplace coefficient 5 46 p value 0 041 constant 244 82 0 000 It is not required for credit to give the constant values We will reject the null hypothesis of no difference at a level of 05 We would not reject at 01 The problem doesn t specify a significance level As long as a student states what their significance level is and correctly chooses whether it is significant or not that is worth the points 3 Run a final regression to test whether the effect of a fireplace is different for houses in university towns vs non university towns Report the coefficients and p values Can you reject the hypothesis of no interaction effect A student MUST use an interaction regression to get this right Minus 1 point minimum for doing otherwise Variable utown 64 27077 0 000 fplace 8 642218 0 001 utown fplace 5 244231 0 150 cons 211 2227 0 000 p value Coef 4 What is the average price of a home in a university town without a fireplace You can calculate by hand or use STATA as a calculator immediately after you run the above regression like this display b cons b utown 275 4935 b 5 points Now regress price on age and sqft This is Model 1 To Model 1 add in a quadratic term for sqft This is Model 2 1 Calculate the F statistic for the hypothesis test that sqft and sqft 2 jointly have no effect on price in Model 2 You can execute this test however you prefer including using STATA s built in test command test sqft 0 sqft2 0 1 sqft 0 2 sqft2 0 F 2 996 275 19 Prob f 0 0000 c 15 points Go back to Model 1 and modify it so that you can determine whether square feet has a different effect in university towns vs non university This is Model 3 1 Is there a statistically significant difference in the effect of sqft in university vs non university towns Yes The difference in the effect is embodied by the interaction of sqft and utown and the p value for the interaction is 0 000 This problems requires using an interaction regression minus 4 points for failure to do this Graders will check output that Model 3 has an interaction and isn t two separate regressions one for when utown 0 or utown 1 While there is some merit to running two regressions you can t use them to figure out whether the interaction is statistically significant 2 A house is located in a non university town The owners build an extension that increases the square footage by 500 sqft What is the change in the predicted value of the house NOTE in the dataset sqft is in units of 100 sqft and that prices are in units of 1000 You can calculate by hand or use STATA as a calculator immediately after you run the above regression like this display 5 b sqft 38 297551 3 An identical house to the above is located in a university town The owners build a 500 sqft extension What is the change in the predicted value of the house display 5 b sqft b sqft utown 44 595101 d 20 points In practice price variables are often transformed with logarithms This is for some practical reasons described in class Generate a a variable called lprice that is the natural log of the price Run Model 3 with lprice in place of price This is Model 4 Recall from class that the change in a log of a variable is approximately equal to the perecentage change of the variable 1 According to Model 4 if there are two identical homes but one is twenty years older than the other what is the approximate percentage difference in prices For a log linear model the elasticity is equal to beta X Therefore after running model 4 you can calculate the elasticity of price with respect to age as follows display 20 b age 0173892 A 1 increase in age lowers the value of a 20 year old house by about 017 While this is a small number it is statistically signficant 2 What is the elasticity of price with respect to square footage when a house is 2500 square feet in size and is not in a university town 3 What is the elasticity of price with respect to square footage when a house is 1500 square feet in size and is not in a university town display 25 b sqft 9036937 display 15 b sqft 54221622 4 What is the elasticity of price with respect to square footage when a house is 2500 square feet in size and is in a university town Here since utown is not equal to zero you must add the coefficients on utown and sqft utown before multiplying by the square footage display 25 b sqft b sqft utown 81399323 A NOTE ABOUT MODEL 4 If you are looking closely at the results you ll …