. reg lhrsemp lavgsal 1scrap lemploy union grant, robust Linear regression Number of obs = 129 F (5, 123) 15.85 II Prob > F = 0.0000 R- squared = 0. 3214 Root MSE = 1. 2019 Robust lhrsemp Coefficient std. err. t P > t [95% conf. interval] lavesal . 3034056 .3544225 0.86 0.394 - .3981519 1.004963 1scrap - .1207844 . 0659512 -1.83 0.069 - .2513308 . 009762 lemploy . 0835461 .1158909 0.72 0.472 - .1458528 .312945 union - .431207 . 2401951 -1.80 0.075 -.9066585 . 0442445 grant 1. 813657 . 2407847 7.53 0.000 1.337038 2. 290275 -Cons -1. 626782 3.539214 -0.46 0.647 -8.632438 5.378875xtreg lhrsemp lavgsal Iscrap lemploy union grant, fe robust note: union omitted because of collinearity. Fixed-effects (within) regression Number of obs 129 11 Group variable: fcode Number of groups = 45 R-squared: obs per group: Within = 0.5907 min = 1 Between = 0.0185 avg = 2.9 Overall = 0.1759 max = 3 F ( 4, 44) 1I 32.37 corr (u_i, Xb ) = -0.5287 Prob > F = 0.0000 (Std. err. adjusted for 45 clusters in fcode) Robust lhrsemp Coefficient std. err. t P> t [95% conf. interval] lavgsal 1.98886 1.168338 1.70 0.096 - .3657705 4.34349 1scrap - . 4892098 . 1810252 -2.70 0. 010 - . 854042 - . 1243775 lemploy - . 4264633 . 2867516 -1.49 0.144 -1. 004373 . 1514465 union (omitted ) grant 1. 824823 . 1891077 9.65 0.000 1. 443702 2. 205945 Cons -16.11956 10.9549 -1.47 0.148 -38.1977 5.958591 sigma_u 1.3530499 sigma e .82820076 rho . 72744972 ( fraction of variance due to u_i). reg lhrsemp lavgsal 1scrap lemploy union grant Source SS df MS Number of obs = 129 F (5, 123) = 11. 65 Model 84.1405954 5 16.8281191 Prob > F = 0.0000 Residual 177. 686407 123 1.44460494 R-squared = 0. 3214 Adj R-squared = 0.2938 Total 261.827003 128 2.04552346 Root MSE = 1. 2019 lhrsemp Coefficient Std. err, t P > t [95% conf. interval] lavgsal .3034056 .3537189 0.86 0.393 - .3967594 1. 003571 1scrap -.1207844 . 0779828 -1.55 0.124 - .2751465 .0335777 lemploy . 0835461 .1193747 0.70 0.485 - . 1527488 . 3198409 union - .431207 .2575803 -1.67 0.097 - .9410714 .0786574 grant 1.813657 . 2669442 6.79 0.000 1. 285257 2.342057 _Cons -1.626782 3.504192 -0.46 0.643 - 8.563115 5.309552The jtrain.dta dataset contains information on job training, and other variables, at a variety of manufacturing facilities. Here is a list with brief definitions of the variables in the data. Please mark your answers a., b., c., d., e. 1. year 1987, 1988, or 1989 2. fcode firm code number 3. employ # employees at plant 4. sales annual sales, $ 5. avgsal average employee salary 6. scrap scrap rate (per 100 items) 7. rework rework rate (per 100 items) 8. tothrs total hours training 9. union =1 if unionized 10. grant =1 if received grant 11. totrain total employees trained 12. hrsemp tothrs/totrain 13. 1scrap log ( scrap) 14. lemploy log (employ) 15. Isales log ( sales) 16. 1rework log ( rework) 17. 1hrsemp log (1 + hrsemp) 18. 1scrap_1 lagged 1scrap; missing 1987 19. grant_1 lagged grant; assumed 0 in 1987 20. lavgsal log (avgsal ) Use the command "xtset fcode year" to inform STATA that this is a panel dataset. Run a pooled regression of lhrsemp on lavgsal Iscrap lemploy union grant a. Report below the coefficient and p-value for union. b. All else equal, a 1% decrease of scrap produces a change in hrsemp. Run a fixed effects regression with the same variables from above, where the fixed effects entities are the firms. For reasons that will be apparent below, I recommend using the xtreg command as you did in homework 6. C. All else equal, when a firm gets a grant this will increase the lhrsemp by -. The confidence interval for this increase is between and d. The F-statistic for the fixed effect variables is: e. You should see that the variable for union membership was dropped from this regression due to perfect multicollinearity. Determine precisely why that happened for this data and explain below