ECON 306 Homework 3 Creighton Mitchell 0874 Don t lose points read these instructions carefully Carefully answer each of the questions below You need to show your work not just the final answer Please make sure your work is legible each problem and step are properly numbered lettered in order You can write or type your answers for the questions Please put your name and PSU ID number at the top of the 1st page You may use as many sheets of paper as you need If you did parts by hand o Scan your entire document including the parts you typed and the parts done by hand o Save the file on your computer PDF is the only acceptable format o Merge the separate PDFs into one file using a service such as PDFMerge Failure to submit a single file will result in points being deducted o Upload it to the CANVAS dropbox for this homework assignment If you typed everything o Save the file on your computer PDF is the only acceptable format and then upload it to the CANVAS dropbox for this homework assignment o Be sure your assignment is all on one file Failure to submit a single file will result in points being deducted Pages must be scanned in proper order 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 52 points total 4 points each part With this assignment you will find a STATA data file called boston dta For reference the variables in this file are nox nitric oxides concentration parts per 10 million rm average number of rooms per dwelling age proportion of owner occupied units built prior to 1940 dis weighted distances to five Boston employment centers ptratio pupil teacher ratio by town lstat percent lower status of population medv median value of owner occupied homes in thousands of dollars Open this dataset within STATA only STATA can open it 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 a Run the following regression 0 1 b Hypothesize the sign of the bias if any resulting from excluding age from the regression Explain your reasoning There is no wrong answer as long as you make a sensible story a I would contend a negative bias meaning that excluding age of a unit units built prior to 1940 would constrict our view of the population of properties on the market Given supply and demand functions this would therefore increase the relative value of the remaining homes Thus a negative bias c Use the data to verify or not your claim from b Break down the bias into its pieces a Running a new regression where we omit both age and average rooms in the dwelling seems to increase the value while decreasing both the coefficient of rm d Now run the regression 0 1 2 3 4 5 6 e At a level of 05 for which if any values of i would you reject the null a Picture hypothesis that i 0 a The coeff of age is 001331 which is the only that will be accepted within our given range Any of the pvalues less than 0 05 we would fail to reject f What is the predicted medv with nox 0 5 rm 4 age 60 dis 3 ptratio 20 and lstat 10 a Predic medv 14 969 b 37 5 17 9 0 5 4 17 4 001 60 1 197 3 1 04 20 579 10 g Redo f but with nox 0 6 What is the difference in predicted medv between these two communities Compare this with the coefficient of nox a 37 5 17 9 0 6 4 17 4 001 60 1 197 3 1 04 20 579 10 b 14 969 13 179 1 79 difference i This reminiscent of a one unit in increase in MEDV s exposure to NOX as shown in the lecture h Ceteris Peribus compared to f what is the impact of reducing the pupil teacher ratio to 18 i 15 259 a 37 5 17 9 0 6 4 17 4 001 60 1 197 3 1 04 18 579 10 b In Qf we got a value of 14 969 c Now we have an updated value of 15 259 for a difference of 29 i Meaning that the high the ptratio the the greater the impact on child performance is i What percentage of the variation in medv is explained by the six X variables a R squared 0 7081 x 100 70 81 Now change the measurement of nox Use the gen command gen noxppm nox 10 and then use this in place of nox in the regression command regress medv noxppm rm age dis ptratio lstat j Compare the coefficient standard error and t ratio for noxppm to that of nox Interpret the difference between this model and the previous a The coefficients have changed by a factor of 10 for nox That can also be said of the standard error as well This is easy to understand because in the gen command we are alternating the total volume of nox meaning that dilution of its value is not present rather the inverse can be said k Also compare the 2 and remaining coefficients Interpret the difference between this model and the original regression model a All else remained the same up to the original decimal points at least Unaltered Now change the variable age to newage gen newage 100 age and then use this in place of age in the original regression command That is execute regress medv nox rm newage dis ptratio lstat l Compare the coefficient standard error and t ratio for newage to that of age Interpret the difference between this model and the previous a The standard error for newage is unaltered but the coefficient otherwise is made positive t ratio had a similar impact going from negative to positive It s worth noting that it is not significantly statiscally as well being less than 5 all else the change in medv would go up with a positive instead of down with a negative attached m Also compare the 2 and remaining coefficients Interpret the difference between this model and the …