Question 4 *** For those of you who are not familiar with the baseball rules, you are allowed to consult with those who are familiar with the baseball rules. Imagine that you are running the agency that represents many professional athletes. You are often involved in renegotiating the contracts for your players. You have decided to evaluate the data collected to support your argument that the player whose contract you are negotiating is currently underpaid. Use the data in strikeout.xls to answer the following questions. a). One of the players that you represent had the lowest number of strike outs in the season. For that reason, you think that that should earn him a raise. To your surprise, the regression estimates show that number of strikeouts has a positive effect on player's salary. The results of this regression analysis are in the table below. Dependent variable: Salary Coefficient S.E T-stat p-value estimate Constant 405.67 120.83 3.35 0.0878 Strike outs 14.863 1.8307 8.11 0.0000 Your assistant suggests that players with many strikeouts usually have very high number of home runs and thus, your estimated model suffers from omitted variable bias. Using the data file, check if there is a positive correlation between number of strikeouts and number of homeruns. Predict what would happen to the coefficient estimate for the number of strikeouts if number of homeruns was included in the model. (this is a throwback to previous module, think about omitted variable bias and use correlations to predict the bias and explain these results). b). Now conduct a regression analysis using ALL of the data provided to predict the salary. Interpret estimated coefficients. Do the signs of coefficients make sense? Explain why you think that's the case. c). Remove the variables that were insignificant in regression from part b). Are the variables that you removed jointly significant? (Hint: you need to test a joint hypothesis for all insignificant coefficients)