Data has been gathered to explain executive salaries from a variety of factors.
ID: 3071621 • Letter: D
Question
Data has been gathered to explain executive salaries from a variety of factors.
Perform a Multiple Regression to predict SALARY from EXPerience, EDUCation, GENDER, NUMberSupported and ASSETS.
a. What is the regression equation? Write an interpretation of the regression equation
b. Calculate the coefficient of determination. How would you interpret this?
c. State the hypotheses to test for the significance of the independent factors. Using t-tests, at alpha= 0.05 determine which factors are significantly related to Executive SALARY
SALARY EXP EDUC GENDER NUMSUP ASSETS 93300 12 15 1 240 170 130000 25 14 1 510 160 88200 20 14 0 370 170 74400 3 19 1 170 170 115300 19 12 1 520 150 70400 14 13 0 420 160 114200 18 18 1 290 170 72600 2 17 1 200 180 108600 14 13 1 560 180 68600 4 16 1 230 160 102000 8 18 1 540 150 101400 19 15 1 90 180 149400 23 16 1 560 180 57100 5 15 0 470 150 87400 3 16 1 340 190 131000 22 17 1 70 200 90300 24 14 0 160 180 115600 22 16 1 160 190 102800 13 18 1 110 180 141900 21 16 1 410 180 90900 10 13 1 370 190 73400 11 12 1 180 170 101000 12 19 1 60 200 85400 10 19 1 60 180 138300 26 17 1 110 200 82300 7 15 1 280 190 85500 7 19 1 110 180 75300 10 19 0 300 170 87500 23 14 0 220 170 127100 12 15 1 570 200 80100 6 16 1 240 180 90900 15 16 0 300 150 109600 15 18 1 260 170 70700 8 13 1 150 160 104400 18 19 0 350 160 71200 2 13 1 370 190 85400 13 14 1 150 160 89300 12 17 0 480 190 124800 21 15 1 310 180 42800 3 12 0 340 150 125000 20 16 1 520 160 122200 20 19 1 200 170 107100 20 17 0 490 160 61000 1 15 0 570 180 59800 2 17 1 70 160 95700 9 17 1 300 160 85600 11 17 0 190 160 88900 21 13 0 500 160 143000 20 20 1 390 170 109200 17 16 0 520 180 156700 24 12 1 530 200 65100 2 17 0 590 190 105900 9 13 1 560 170 74300 2 18 0 600 190 79300 13 12 0 390 170 106600 14 18 1 110 170 106400 18 13 1 190 190 77400 10 14 1 110 160 129400 21 13 1 430 190 82600 11 14 0 440 150 126100 26 15 1 210 190 121900 22 18 1 320 160 96200 3 16 1 560 180 128900 17 18 1 450 190 72200 2 16 1 410 180 58800 4 18 0 70 150 79300 8 17 1 90 190 96100 13 15 1 290 160 94900 3 18 1 530 180 89000 13 16 0 420 170 108800 25 19 0 150 200 95300 11 15 1 500 190 71200 2 17 0 430 190 173400 26 17 1 570 190 107000 20 20 1 90 150 100000 19 12 1 340 160 100700 12 13 1 440 170 152800 22 18 1 500 160 95300 13 13 0 570 180 77300 2 15 1 560 190 84600 15 14 1 160 170 92600 12 13 1 390 190 85900 13 19 0 370 200 79400 5 17 1 330 160 80100 8 17 0 560 170 114100 21 20 0 590 180 78500 5 16 1 290 200 87300 9 18 0 440 180 102900 19 15 0 480 190 116300 23 19 1 130 150 51500 3 12 0 440 190 106500 13 19 1 310 150 109000 22 17 0 370 200 66600 9 12 0 180 160 111100 7 19 1 520 200 83100 10 18 0 90 180 159500 25 18 1 590 160 122500 10 19 1 480 200 67300 3 19 1 80 160 97900 16 17 0 380 160Explanation / Answer
Here we will use the multiple regression analysis of EXCEL.
THe excel regression output is given below
(a)
Hre the regression equationis
Salary = -42495.3 + 2635.486 * Exp + 2666.489 * EDUC + 21981.03 * GENDER + 55.1606 * NUMSUP + 168.8869 * ASSETS
(b) Here the coeffficient of determination is 0.91915
so here we can interpret it as there is 91.915% variability could be explained by the independt variables.
(c) Here at alpha = 0.05,we will checkthe p - value of each independent variable and as we see that p - value for all the independent variables are less than 0.05 so each inddepepndent variable is significant here.
SUMMARY OUTPUT Regression Statistics Multiple R 0.958728 R Square 0.919159 Adjusted R Square 0.914859 Standard Error 7357.702 Observations 100 ANOVA df SS MS F Significance F Regression 5 5.79E+10 1.16E+10 213.7551 1.02E-49 Residual 94 5.09E+09 54135775 Total 99 6.29E+10 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -42495.3 9898.371 -4.29316 4.28E-05 -62148.8 -22841.9 -62148.8 -22841.9 EXP 2635.586 100.8157 26.14262 6.57E-45 2435.414 2835.758 2435.414 2835.758 EDUC 2666.489 326.8269 8.158719 1.48E-12 2017.566 3315.411 2017.566 3315.411 GENDER 21981.03 1601.493 13.72534 3.53E-24 18801.23 25160.83 18801.23 25160.83 NUMSUP 55.1606 4.642538 11.88156 2.01E-20 45.94273 64.37847 45.94273 64.37847 ASSETS 168.8869 48.69802 3.468045 0.000793 72.19586 265.578 72.19586 265.578Related Questions
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