QUESTION:

An interested researcher wants to prove that for every 1-year increase in work experience (WE) of an employee, the salary increases by more than Rs 3300. Can you check (at 5% significance level) if the theory (i.e. salary increasing by more than 3300 for an additional year of work experience) of the researcher is true or not for the entire population? Show all your workings clearly.

A research study wants to investigate the impact of Gender (Female=1, Male=0) and Work Experience (WE - measured in years) on the Salary (measured in Rs) earned by people. An additional interaction variable Gender WE= Gender* WE is also created. Following are the partial regression results (run on a sample of n=30): Model R R Square Model Summary Adjusted R Square Std. Error of the Durbin-Watson Estimate 1 3354.2910 631 a. Predictors: (Constant), GenderWE, WE, Gender b. Dependent Variable: Salary ANOVA Model Sum of Squares df Mean Square F Sig. Regression 1 Residual 292532962.665 26 Total 3575351750.000 29 a. Dependent Variable: Salary b. Predictors: (Constant), GenderWE, WE, Gender Coefficientsa Model t Unstandardized Coefficients Standardized Coefficients Sig. 95.0% Confidence Interval for B Collinearity Statistics B Std. Error Beta Tolerance VIF Lower Bound Upper Bound (Constant) 13443.895 1539.893 10278.600 16609.191 Gender -7757.751 2717.884 - 348 -13344.442 -2171.059 .212 4.727 1 WE 3523.547 383.643 2734.956 4312.137 .730 1.369 -4443.662 -1384.154 .203 4.916 GenderWE -2913.908 744.214 a. Dependent Variable: Salary N Mean 40 Gender WE Salary GenderWE Valid N (list wise) 30 30 30 30 30 Descriptive Statistics Minimum Maximum 0 1 1.00 7.0 4100.00 39900.00 .00 6.00 3.3333 18395.0000 1.2667 Std. Deviation 498 1.89979 11103.51257 1.85571 Normal P-P Plot of Regression Standardized Residual Dependent Variable: Salary Scatterplot Dependent Variable: Salary 101 08 o 0.6 Expected Cum Prob OOOOO o gression Standardized Residual 024 OD 02 0.5 08 Observed Cum Prob Regression Standardized Predicted Value Annexure A: S. No. Gender WE Salary Residual Deleted Residual Standardized Residual Studentized Residual 1 1 2 2 1 3 1 3 1 4 1 3 5 1 4 Studentized Deleted Residual -0.03309 0.36295 1.18325 0.61091 0.61619 0.16852 -1.96492 -1.54986 -3.19862 -2.07987 0.1393 0.51034 6 1 7 0 6 2 3 8 0 9 0 4 0 10 11 2 4 0 12 13 3 1 0 1.08725 0.87588 14 0 4 15 0 6800-105.42169-121.52778 8700 1184.9398 1294.079 9700 3404.2169 4557.2581 9500 1984.9398 2167.7632 10100 1975.3012 2215.5405 9800 456.0241 727.88462 14500 -5990.9884 -6532.1712 19100 -4914.5349-5217.9012 18600 -8938.0814 -9504.4822 14200 -6290.9884 -6859.271 28000 461.9186 491.19011 25700 1685.4651 1789.5062 20350 3382.5581 3904.698 30400 2861.9186 3043.2767 19400 2432.5581 2808.0537 22100 1609.0116 1754.3582 20200 3232.5581 3731.5436 17700 732.55814 845.63758 34700 114.82558 133.67174 38600 491.27907 630.59701 39900 1791.2791 2299.2537 38300 191.27907 245.52239 26900 2885.4651 3063.5803 31800 4261.9186 4531.9938 8000 -734.33735 -923.48485 8700 -34.33735 -43.18182 6200 -1315.0602-1436.1842 4100-3415.0602-3729.6053 5000 -1905.4217-2196.5278 4800 -1495.7831-2002.4194 -0.03143 0.35326 1.01488 0.59176 0.58889 0.13595 -1.78607 -1.46515 -2.66467 -1.8755 0.13771 0.50248 1.00843 0.85321 0.72521 0.47969 0.96371 0.21839 0.03423 0.14646 0.53403 0.05703 0.86023 1.27059 -0.21892 -0.01024 -0.39205 -1.01812 -0.56805 -0.44593 1 2 1 -0.03374 0.36917 1.17425 0.61841 0.62367 0.17176 -1.86499 -1.50969 -2.7478 -1.95838 0.14201 0.51776 1.08347 0.87983 0.77917 0.50088 1.03542 0.23465 0.03694 0.16594 0.60503 0.06461 0.88638 1.31023 -0.24551 -0.01148 -0.40971 -1.06397 -0.60991 -0.51595 16 0 17 18 0 1 6 19 0 0 20 21 7 7 0 0 7 22 23 0.77312 0.49355 1.03692 0.23033 0.03622 0.1628 0.5975 0.06336 0.88261 1.32942 -0.24102 -0.01126 -0.40306 -1.06679 -0.60239 -0.50854 0 3 24 0 4 1 5 1 25 26 27 28 29 5 3 1 1 3 1 2 30 1 1 1 Annexure B: uzo Gen der W E Sala ry Mahala nobis distance Cook Lever 's age dista Value nce S Standar dized DfFit Standar Standar dized dized DfBeta DfBeta (interce (Gender pt) 0 -0.00951 Standar dized DfBeta (WE) Standar dized DfBeta (Gender WE) 0.00675 1 1 2 2.87671 0.099 2 -0.01293 0 2 1 3 1.47912 0.051 0.11015 0 0.04794 0 -0.0103 3 1 1 6.37068 0.219 68 0.68864 0 0.55981 0 0.000 04 0.003 14 0.116 76 0.008 81 0.011 83 0.004 -0.48323 4 1 3 1.47912 0.051 0.18541 0 0.08069 0 -0.01733 5 1 4 2.17791 0.21489 0 -0.0097 0 0.08859 6 1 6 9.86466 0.13012 0 -0.06332 0 0.09827 7 0 2 1.43595 -0.59057 -0.53917 0.30548 0.33896 -0.17474 8 0 3 0.71938 -0.38507 -0.26292 0.14897 0.08118 -0.04185 9 0 4 0.76153 -0.8052 -0.2193 0.12425 -0.20958 0.10804 1 0 0 2 1.43595 -0.62511 -0.57071 0.32335 0.35879 -0.18496 1 1 0 4 0.76153 0.03507 0.00955 -0.00541 0.00913 -0.00471 0 3 680 0 870 0 970 0 950 0 101 00 980 0 145 00 191 00 186 00 142 00 280 00 257 00 203 50 304 00 194 00 221 00 202 00 177 00 347 00 386 00 399 00 383 00 269 00 0.71938 0.12679 0.08657 -0.04905 -0.02673 0.01378 0 1 2.91124 0.42717 0.42163 -0.23888 -0.3266 0.16836 0 4 0.76153 0.22049 0.075 1 0.340 16 0.049 52 0.024 81 0.026 26 0.049 52 0.026 26 0.024 81 0.100 39 0.026 26 0.100 39 0.049 52 0.100 39 0.100 39 0.107 66 0.187 6 0.187 6 0.187 6 0.024 81 0.06005 -0.03402 0.05739 -0.02959 0 1 2.91124 0.078 55 0.035 17 0.119 62 0.086 61 0.000 32 0.004 14 0.045 3 0.012 26 0.023 43 0.005 67 0.041 37 0.002 12 0.000 06 0.001 95 0.025 95 0.000 3 0.012 12 0.30375 0.29981 -0.16987 -0.23223 0.11972 0 2 1.43595 0.14834 0.13543 -0.07673 -0.08514 0.04389 0 1 2.91124 0.40739 0.40211 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 -0.22782 -0.31147 0.16057 0 1 2.91124 0.0905 0.08932 -0.05061 -0.06919 0.03567 0 6 3.122 0.01467 -0.00507 0.00287 0.01142 -0.00589 0 7 5.44031 0.08669 -0.04205 0.02382 0.07501 -0.03867 0 7 5.44031 0.31818 -0.15431 0.08743 0.27529 -0.14191 0 7 5.44031 0.03374 -0.01636 0.00927 0.02919 -0.01505 0 3 0.71938 0.21929 0.14973 -0.08483 -0.04623 0.02383 0 4 0.76153 0.33466 0.09115 -0.05164 0.08711 -0.0449 1 5 4.97309 0.026 26 0.171 49 0.171 49 -0.12232 0 0.0422 0 -0.08072 1 5 4.97309 -0.00571 0 0.00197 0 -0.00377 Anna ON ano 1 3 318 00 800 0 870 0 620 0 410 0 500 0 480 0 1.47912 0.027 2 0.003 88 0.000 01 0.003 87 0.026 07 0.014 21 0.022 54 0.051 -0.12232 0 -0.05324 0 0.01144 1 3 1.47912 0.051 -0.32376 0 -0.1409 0 0.03027 2 8 2 9 1 2 2.87671 -0.23545 0 -0.17311 0 0.12293 0.099 2 0.219 68 1 1 6.37068 -0.29597 0 -0.2406 0 0.20769 A research study wants to investigate the impact of Gender (Female=1, Male=0) and Work Experience (WE - measured in years) on the Salary (measured in Rs) earned by people. An additional interaction variable Gender WE= Gender* WE is also created. Following are the partial regression results (run on a sample of n=30): Model R R Square Model Summary Adjusted R Square Std. Error of the Durbin-Watson Estimate 1 3354.2910 631 a. Predictors: (Constant), GenderWE, WE, Gender b. Dependent Variable: Salary ANOVA Model Sum of Squares df Mean Square F Sig. Regression 1 Residual 292532962.665 26 Total 3575351750.000 29 a. Dependent Variable: Salary b. Predictors: (Constant), GenderWE, WE, Gender Coefficientsa Model t Unstandardized Coefficients Standardized Coefficients Sig. 95.0% Confidence Interval for B Collinearity Statistics B Std. Error Beta Tolerance VIF Lower Bound Upper Bound (Constant) 13443.895 1539.893 10278.600 16609.191 Gender -7757.751 2717.884 - 348 -13344.442 -2171.059 .212 4.727 1 WE 3523.547 383.643 2734.956 4312.137 .730 1.369 -4443.662 -1384.154 .203 4.916 GenderWE -2913.908 744.214 a. Dependent Variable: Salary N Mean 40 Gender WE Salary GenderWE Valid N (list wise) 30 30 30 30 30 Descriptive Statistics Minimum Maximum 0 1 1.00 7.0 4100.00 39900.00 .00 6.00 3.3333 18395.0000 1.2667 Std. Deviation 498 1.89979 11103.51257 1.85571 Normal P-P Plot of Regression Standardized Residual Dependent Variable: Salary Scatterplot Dependent Variable: Salary 101 08 o 0.6 Expected Cum Prob OOOOO o gression Standardized Residual 024 OD 02 0.5 08 Observed Cum Prob Regression Standardized Predicted Value Annexure A: S. No. Gender WE Salary Residual Deleted Residual Standardized Residual Studentized Residual 1 1 2 2 1 3 1 3 1 4 1 3 5 1 4 Studentized Deleted Residual -0.03309 0.36295 1.18325 0.61091 0.61619 0.16852 -1.96492 -1.54986 -3.19862 -2.07987 0.1393 0.51034 6 1 7 0 6 2 3 8 0 9 0 4 0 10 11 2 4 0 12 13 3 1 0 1.08725 0.87588 14 0 4 15 0 6800-105.42169-121.52778 8700 1184.9398 1294.079 9700 3404.2169 4557.2581 9500 1984.9398 2167.7632 10100 1975.3012 2215.5405 9800 456.0241 727.88462 14500 -5990.9884 -6532.1712 19100 -4914.5349-5217.9012 18600 -8938.0814 -9504.4822 14200 -6290.9884 -6859.271 28000 461.9186 491.19011 25700 1685.4651 1789.5062 20350 3382.5581 3904.698 30400 2861.9186 3043.2767 19400 2432.5581 2808.0537 22100 1609.0116 1754.3582 20200 3232.5581 3731.5436 17700 732.55814 845.63758 34700 114.82558 133.67174 38600 491.27907 630.59701 39900 1791.2791 2299.2537 38300 191.27907 245.52239 26900 2885.4651 3063.5803 31800 4261.9186 4531.9938 8000 -734.33735 -923.48485 8700 -34.33735 -43.18182 6200 -1315.0602-1436.1842 4100-3415.0602-3729.6053 5000 -1905.4217-2196.5278 4800 -1495.7831-2002.4194 -0.03143 0.35326 1.01488 0.59176 0.58889 0.13595 -1.78607 -1.46515 -2.66467 -1.8755 0.13771 0.50248 1.00843 0.85321 0.72521 0.47969 0.96371 0.21839 0.03423 0.14646 0.53403 0.05703 0.86023 1.27059 -0.21892 -0.01024 -0.39205 -1.01812 -0.56805 -0.44593 1 2 1 -0.03374 0.36917 1.17425 0.61841 0.62367 0.17176 -1.86499 -1.50969 -2.7478 -1.95838 0.14201 0.51776 1.08347 0.87983 0.77917 0.50088 1.03542 0.23465 0.03694 0.16594 0.60503 0.06461 0.88638 1.31023 -0.24551 -0.01148 -0.40971 -1.06397 -0.60991 -0.51595 16 0 17 18 0 1 6 19 0 0 20 21 7 7 0 0 7 22 23 0.77312 0.49355 1.03692 0.23033 0.03622 0.1628 0.5975 0.06336 0.88261 1.32942 -0.24102 -0.01126 -0.40306 -1.06679 -0.60239 -0.50854 0 3 24 0 4 1 5 1 25 26 27 28 29 5 3 1 1 3 1 2 30 1 1 1 Annexure B: uzo Gen der W E Sala ry Mahala nobis distance Cook Lever 's age dista Value nce S Standar dized DfFit Standar Standar dized dized DfBeta DfBeta (interce (Gender pt) 0 -0.00951 Standar dized DfBeta (WE) Standar dized DfBeta (Gender WE) 0.00675 1 1 2 2.87671 0.099 2 -0.01293 0 2 1 3 1.47912 0.051 0.11015 0 0.04794 0 -0.0103 3 1 1 6.37068 0.219 68 0.68864 0 0.55981 0 0.000 04 0.003 14 0.116 76 0.008 81 0.011 83 0.004 -0.48323 4 1 3 1.47912 0.051 0.18541 0 0.08069 0 -0.01733 5 1 4 2.17791 0.21489 0 -0.0097 0 0.08859 6 1 6 9.86466 0.13012 0 -0.06332 0 0.09827 7 0 2 1.43595 -0.59057 -0.53917 0.30548 0.33896 -0.17474 8 0 3 0.71938 -0.38507 -0.26292 0.14897 0.08118 -0.04185 9 0 4 0.76153 -0.8052 -0.2193 0.12425 -0.20958 0.10804 1 0 0 2 1.43595 -0.62511 -0.57071 0.32335 0.35879 -0.18496 1 1 0 4 0.76153 0.03507 0.00955 -0.00541 0.00913 -0.00471 0 3 680 0 870 0 970 0 950 0 101 00 980 0 145 00 191 00 186 00 142 00 280 00 257 00 203 50 304 00 194 00 221 00 202 00 177 00 347 00 386 00 399 00 383 00 269 00 0.71938 0.12679 0.08657 -0.04905 -0.02673 0.01378 0 1 2.91124 0.42717 0.42163 -0.23888 -0.3266 0.16836 0 4 0.76153 0.22049 0.075 1 0.340 16 0.049 52 0.024 81 0.026 26 0.049 52 0.026 26 0.024 81 0.100 39 0.026 26 0.100 39 0.049 52 0.100 39 0.100 39 0.107 66 0.187 6 0.187 6 0.187 6 0.024 81 0.06005 -0.03402 0.05739 -0.02959 0 1 2.91124 0.078 55 0.035 17 0.119 62 0.086 61 0.000 32 0.004 14 0.045 3 0.012 26 0.023 43 0.005 67 0.041 37 0.002 12 0.000 06 0.001 95 0.025 95 0.000 3 0.012 12 0.30375 0.29981 -0.16987 -0.23223 0.11972 0 2 1.43595 0.14834 0.13543 -0.07673 -0.08514 0.04389 0 1 2.91124 0.40739 0.40211 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 -0.22782 -0.31147 0.16057 0 1 2.91124 0.0905 0.08932 -0.05061 -0.06919 0.03567 0 6 3.122 0.01467 -0.00507 0.00287 0.01142 -0.00589 0 7 5.44031 0.08669 -0.04205 0.02382 0.07501 -0.03867 0 7 5.44031 0.31818 -0.15431 0.08743 0.27529 -0.14191 0 7 5.44031 0.03374 -0.01636 0.00927 0.02919 -0.01505 0 3 0.71938 0.21929 0.14973 -0.08483 -0.04623 0.02383 0 4 0.76153 0.33466 0.09115 -0.05164 0.08711 -0.0449 1 5 4.97309 0.026 26 0.171 49 0.171 49 -0.12232 0 0.0422 0 -0.08072 1 5 4.97309 -0.00571 0 0.00197 0 -0.00377 Anna ON ano 1 3 318 00 800 0 870 0 620 0 410 0 500 0 480 0 1.47912 0.027 2 0.003 88 0.000 01 0.003 87 0.026 07 0.014 21 0.022 54 0.051 -0.12232 0 -0.05324 0 0.01144 1 3 1.47912 0.051 -0.32376 0 -0.1409 0 0.03027 2 8 2 9 1 2 2.87671 -0.23545 0 -0.17311 0 0.12293 0.099 2 0.219 68 1 1 6.37068 -0.29597 0 -0.2406 0 0.20769