Harrison Hayes PappasHarrison Hayes Pappas_$.Penn State UniversityV$. Name (Last, First) _________________________________________ Email ID: ____________________@psu.edu ECON 306 Homework 6 Due: Thursday, December 1, 2016 Instructions: Please print out and complete the following assignment writing your answers clearly and showing your work directly on the assignment. Please keep a log of your work in STATA and print out and attach all of your results. Use a highlighter to highlight all of your commands in STATA (this will make it easier for the graders to see your work). Follow directions carefully (underlining or circling where indicated in your STATA output). Be sure to turn the assignment in at the beginning of class on Thursday, December 1. Late homeworks cannot be accepted. 1. The data set footballcoach.xlsx contains data on football coaches and whether or not they were fired. The variable firedcoach is a dummy variable equal to 1 if the football coach was fired during or after the season and the variable winpct is the winning percentage of the coach's team. Estimate the linear probability model: firedcoach = f(winpct) in STATA. (Include your STATA work). a. Report the values of the coefficient and pvalue for winpct: (4 points) The coefficient for WinPct is -0.8205 and the p-value is 0.00 b. Let's say a coach's winning percentage increases by 0.10. In words, express what the beta coefficient for \"winpct\" means for this change using the value estimated by STATA. (4 points) The beta coefficient means that for every 1 unit increase in winning percentage the chances of coach getting fired reduces by 0.8205 units. So, when winning percentage increases by 0.1, the chances of the coach getting fired reduces by 0.08205. c. In STATA, create a scatter for the observed data in this dataset and include the line of best fit. (Hint: See page 95 of the coursepack). (4 points) The scatter plot and line of best fit is shown as 1 .5 0 -.5 0 .2 .4 WinPct Fitted values .6 .8 1 FiredCoach d. What is the R2 estimated from the linear probability model? (3 points) The R2 estimated for the linear probability model is 0.1708. This means that only 17.08% of variability in FiredCoach is explained by the winning percentage (WinPct) e. Using the method shown in class, calculate Rp2. (Show the work that you do in STATA) (5 points) Rp2 = 0.0597. Rp2 = (467/564) = 0.828 So, we can say that 82.8% of choices were explained correctly. 2. In this next model, replace winpct with wins (number of wins in the season). Now estimate the logit model: firedcoach = f(wins) in STATA. (Include your STATA work) a. Report the values of the coefficient and pvalue for \"wins\": (4 points) The coefficient for win is -0.4473 and the p-value is 0.00 b. In words, express what the beta coefficient for \"wins\" means using the \"rough estimate of 0.25\" approach using the values estimated by STATA. (4 points) When the value if wins is 0.25 Log(FiredCoach) = 1.4863 - 0.4473*0.25 = 1.3744 So, the conditional logit of being fired when the wins is 0.25 is 1.3744 So, for 1 unit increase in the value of Wins the change in log odds is a decrease of 0.4473