ECON 306 Homework 4 Creighton Mitchell ID 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 It will generate many pages of output Here is how you 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 You are encouraged to save paper here you may print this section with a small font double sided 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 50 points total In this exercise we will examine whether a teacher s physical attractiveness has any impact on student course evaluations The dataset to use is called teachingratings and a description of the variables is available as well You can access these through the course website Use an 05 for hypothesis testing We ll first examine whether our control variables seem to have any predictive power for ratings a 10 points We ll start with some basic dummy variable regressions to test for differences between groups 1 Regress course eval on minority Report the coefficients and p values Do minority instructors have significantly different course evaluations compared to non minorities B1 coeff 12 P value 0 099624 H0 minority 0 Ha minority doesn t equal 0 T crit 1 96 T stat 1 65 If t stat is greater than 1 96 or smaller than negative 1 96 we will reject our null hypo Due to the data we can t reject null hypo This means there is no significant difference in the course evaluation of minority or the latter holding other factors constant 2 Regress course eval on female Report the coefficients and p values Do females have significantly different course evaluations from males B1 coeff 12 P value 0 099624 H0 female 0 Ha female doesn t equal 0 T crit 1 96 T stat 3 25 If t stat is greater than 1 96 or smaller than negative 1 96 we will reject our null hypo Due to the data we reject null hypo our t value is 1 96 and our calc t value is 3 25 This means there is a significant difference in the wages of males and females holding other factors constant 3 Run a final regression to test whether the effect of being a minority changes depending on whether the person is female Report the coefficients and p values Can you reject the hypothesis of no effect No we can reject null hypo of no effect the pvalue is greater than 5 level of significance Due to the fact that female have a negative coefficient and adding minority does not produce a positive effect as well Therefore minority isn t significant b 10 points Now regress course eval on beauty age age 2 you ll need to create this nenglish female minority onecredit Are any variables not statistically significant Which This is Model 1 Use Model 1 to answer the following 1 Calculate an F test for the hypothesis that age and age 2 jointly have no effect on course eval You can execute this test however you prefer i F 2 455 0 73 ii F crit 3 0155431 2 Calculate an F test that female and minority have an equal impact on course eval You can execute this test however you prefer F 2 455 10 44 F crit 3 0155431 c 15 points Modify Model 1 so that you can determine whether beauty has a different effect for women than for men This is Model 2 Report the coefficient and p value for the interaction variable Can you reject the hypothesis of no effect of the interaction Use Model 2 to answer the following 1 Professor Smith is a man He isn t very handsome He undergoes plastic surgery which raises his beauty from one standard deviation below the mean to one standard deviation above What is the predicted change in his course evaluations Note you will have to figure out how to calculate a standard deviation in STATA It isn t hard Also note that the average beauty level in the data has been scaled to equal zero The predicted change will be b1 1 575 0 22 1 576 less than or equal to 0 34672 2 Repeat part 1 for Professor Jones who is a woman For Professor Jones 1 576 is the one SD below the mean Predicted change beauty 1 576 female 1 576 0 22 1 576 131 1 576 less than or equal to 0 143416 d 15 points Go back to Model 1 Add two variables to Model 1 that will allow you to determine whether age has a different effect for women than for men on course evaluations Note since age appears twice in Model 1 you will need to create the interaction for both age and age 2 This is Model 3 Report the coefficients and p values for the interaction terms Can you reject the hypothesis of no effect of the interactions Use Model 3 results to answer the following Age fem 1007449 P 0 077 Age2 fem 0008894 P 0 149 We cannot reject null hypo 1 Professor Thomas a man begins his teaching career at age 32 Assuming his beauty measure and all other variables is unchanged over his career what is the predicted change in his course eval score when he retires at age 65 age 65 age2 65 0 0795232 65 0 0007679 65 2 1 9235233 predicted change 2 Repeat 1 for Professor Gomez …