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Q5 (15 points) 12.92 Agreeableness, gender, and wages. Do agreeable indi- @ viduals get paid less, on average, than those who are less was agreeable on the job? And is this gap greater for males than for females? These questions were addressed in the Journal of Personality and Social Psychology (February 2012). Several variables were measured for each in a sample of individuals enrolled in the National Survey of Midlife Development in the US. Three of these variables are: (1) level of agreeableness score (where higher scores indicate a greater level of agreeableness), (2) gender (male or female), and (3) annual income (dollars). The research- ers modeled mean income, E (y), as a function of both agreeableness score (x1) and a dummy variable for gender (x2 = 1 if male, 0 if female). Data for a sample of 100 in- dividuals (simulated, based on information provided in the study) are saved in the file. The first 10 observations are listed in the accompanving table. a. Fit a multiple regression model using x1,x2 as independent variables, and test the hypothesis if income would decrease as agreeableness score increases. b. If you would like to test the hypothesis the rate of decrease of income with agreeableness score would be steeper for males than for females, how would you modify the model? Please fit a regression model to test the hypothesis. c. Which model, a or b is better? Please explain. Gender Agree Income 1 3 44770 . 9 51 480 co 39600 3. 3 24370 3. 6 15460 3 . 8 43730 3. 2 48330 2. 5 25970 17120 201 40 19190 53330 28950 20020 BOOHOO O O HOO O 12240 24480 69080 22020 26160 49550 48000 37670 18950 55920 16310 30590 47450 58090 14620 BOOHOHOOH OH ONEHOHOOOK 62760 17600 53820 15280 15740 29000 26850 52810 46000 25680 43590 54050 16700 41560 51770 251 40 32410 0 14390 36480 21640 19390 25810 66670 45330 11150 40200 OOHOH OOH OH HOO OK 26230 32300 56140 20800 49360 22160 19880 61840 11030 52380 44690 51410 4. 3 34340 49650 3. 1 42910 3. 4 44620 2. 7 61980 3 . 21850 28260 54790 35990 53400 13320 51840 44440 28120 54530 19400 45970 23290 57690 32700 30130 44080 57830 15630 34980 61390 21720 55750 OHHHOHOHOO 15840 36040 27020 47510 22220