Name Last First Economics 306 Midterm 2 Spring 2015 100 Points 75 Minutes Instructions Answer the following questions as clearly as you can Circle your answers Partial credit is available but we cannot give partial credit unless you show your work You do not need to write out every detail but give a clear indication of how you are making your calculations For problems with many parts where you use information from earlier in the problem to answer the question you can receive full credit if you do the correct work but use the wrong numbers The clearer you are in your explanation the more straightforward this part of the grading will be You may use any type of hand held calculator All other electronic devices are prohibited DO NOT OPEN UNTIL I START THE TEST Statement of Academic Integrity I understand that cheating on this exam or helping anyone to cheat is a violation of the Penn State policy on academic integrity I understand that if I am caught cheating it could result in academic and or disciplinary action including a mark on my transcript It is also simply ethically wrong to cheat I will not cheat on this exam or knowingly let anyone cheat from my work Signature Date Part 1 9 questions 5 points each 45 points total Suppose we have a large dataset on high school students Amongst the variables in this dataset are measures of cumulative grade point average cumgpa a dummy variable for gender female 1 if the student is female 0 otherwise and a dummy variable for whether the student has a job job 1 if the student is has a job 0 otherwise We execute a few basic regressions for the dependent variable cumgpa and produce the following output in STATA Model 1 coefficients only regress cumgpa job if female 0 cumgpa Coef Std Err t P t 95 Conf Interval job 1764003 0591281 2 98 0 003 0602197 2925809 cons ddddddddd 0504962 0 000 Model 2 coefficients only regress cumgpa job if female 1 cumgpa Coef Std Err t P t 95 Conf Interval job 499555 1150419 4 34 0 000 2722306 7268793 cons 2 294074 1042506 22 01 0 000 2 088074 2 500075 Model 3 coefficients only gen fem job female job regress cumgpa female job fem job cumgpa Coef Std Err t P t 95 Conf Interval female aaaaaaaa 1203879 job bbbbbbbb 0582736 fem job cccccccc 1342717 cons 2 174733 0497664 43 70 0 000 2 077005 2 272461 Model 3 includes the variable Female Job and an interaction of Female and Job Fem Job Some of the STATA output has been concealed 0 322 0 003 0 016 a What is the value of the term bbbbbb This is the effect of job when female 0 or 1764003 b What is the value of the term aaaaaaa This is the effect of female when job 0 This is the difference between the constants in model 1 and 2 2 294074 2 174733 11934125 c What is the value of the term ccccccc This is the difference between the effect of job when female 1 and the effect of job when female 0 or 499555 1764003 324 d What is the value of the term ddddddd This is the constant for the model where F 0 which equals the constant from Model 3 2 175 e Suppose the result for ccccccc is 30 it isn t Given everything else on the printout is correct what is the p value for a hypothesis test that the coefficient on Fem Job 0 Hint you can use the attached z distribution because the sample size is large The test statistic would be HALF POINTS FOR THIS The probability of exceeding this value from the z table is 0129 The p value for a 2 tailed test is twice this number or 0258 DON T PENALIZE ROUNDING ADDITIONAL GRADING NOTE THE TABLE HAS A P VALUE OF 016 ON IT AND IN THE QUESTION I SAID TO ASSUME THAT EVERYTHING ELSE ON THE TABLE WAS CORRECT SO IF A STUDENT ANSWERS 016 THAT IS ALSO CORRECT EVEN THOUGH IT S NOT WHAT I WANTED f Suppose the answer to aaaaaaa is 08 and bbbbbb is 15 they aren t Given everything else on the printout is correct what is the average value of cumgpa for a Male who has a Job This is the predicted value when F 0 job 1 Or 2 174733 15 2 324733 We would like to study how a student s performance on a standardized test the SAT is related to GPA We therefore run a new version of the regression including data on SAT performance Model 4 and get the following coefficients only shown Model 4 regress cumgpa female job fem job sat cumgpa Coef Std Err t P t 95 Conf Interval female 0784467 1132625 0 69 0 489 143971 3008644 job 0837357 0616983 1 36 0 175 2048949 0374234 fem job 3489059 1262577 2 76 0 006 1009691 5968428 sat 0013141 0001434 9 17 0 000 0010325 0015957 cons 1 199383 1162498 10 32 0 000 9710991 1 427667 g What is the t statistic for a hypothesis test that the effect of SAT on GPA is zero Yes this is as easy as it looks 9 17 h Comparing Model 3 to Model 4 what is the implied sign of the correlation between SAT and Female Hint Use what you know about omitted variable bias Positive Including SAT has lowered the value of the coefficient on female That is it implies that there had been a positive bias resulting from the omission of SAT Since SAT has a positive coefficient we know from our general formula for the bias that SAT and female must have a positive relationship i In words explain what the variable fem job is showing about the relationship between gender jobs and gpa Any interaction tries to show whether or not the effect of one variable changes based on the value of a second variable Here fem job can be interpreted as the difference in the effect of a job on GPA for women vs men Equivalently it can be interpreted as the difference in the effect on GPA of being a woman for those with a job vs no job The value here is positive and significant indicating that jobs raise women s GPAs vs men s and that being a woman is more beneficial to GPA when they have a job than when they don t Part 2 8 questions 5 points each except as indicated 45 points total Suppose we are investigating determinants of housing prices We have data on prices distance from the nearest interstate highway instst size of the property area land the number of square feet of the house sqft the number of rooms and age We run the following regression Model 1 with lprice as the dependent variable Important Note Any variable with a prefix of l is a natural log regress lprice lintst lland sqft rooms age agesq Source SS df MS Number of obs 321 F 6 314 81 56 …