3 Perform a regression analysis using compa as the dependent variable and the same independent variables as used in question 2. Show the result, and interpret your findings by answering the same questions. Note: be sure to include the appropriate hypothesis statements. Regression hypotheses Ho: Ha: Coefficient hyhpotheses (one to stand for all the separate variables) Ho: Ha: Place D94 in output box. Interpretation: For the Regression as a whole: What is the value of the F statistic: What is the p-value associated with this value: Is the p-value < 0.05? Do you reject or not reject the null hypothesis: What does this decision mean for our equal pay question: For each of the coefficients: What is the coefficient's p-value for each of the variables: Is the p-value < 0.05? Do you reject or not reject each null hypothesis: What are the coefficients for the significant variables? Using only the significant variables, what is the equation? Is gender a significant factor in compa: If so, who gets paid more with all other things being equal? How do we know? Intercept Compa = Midpoint Age Perf. Rat. Service Gender Degree ID Salary Compa Midpoint Age 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 56.5 28.3 34 64.5 46.6 75.6 41.6 24.6 74.6 24 24.3 57.9 41.9 24.5 23.1 41.1 71.8 34.2 23.8 34.3 78.5 54.9 23.3 55.9 23.7 23.8 38.7 76.7 75.9 48.5 22.3 27 61.4 27.8 22.8 24.7 23.3 56.8 36.1 24 47.3 21.9 75.6 57.2 53.1 58.1 61 64.6 66.3 57.5 0.992 0.913 1.097 1.132 0.971 1.129 1.040 1.070 1.114 1.044 1.055 1.015 1.047 1.066 1.005 1.027 1.259 1.104 1.036 1.106 1.171 1.143 1.015 1.165 1.029 1.036 0.967 1.145 1.133 1.011 0.970 0.871 1.077 0.898 0.992 1.075 1.014 0.997 1.165 1.045 1.182 0.950 1.128 1.003 1.107 1.019 1.071 1.134 1.163 1.008 57 31 31 57 48 67 40 23 67 23 23 57 40 23 23 40 57 31 23 31 67 48 23 48 23 23 40 67 67 48 23 31 57 31 23 23 23 57 31 23 40 23 67 57 48 57 57 57 57 57 34 52 30 42 36 36 32 32 49 30 41 52 30 32 32 44 27 31 32 44 43 48 36 30 41 22 35 44 52 45 29 25 35 26 23 27 22 45 27 24 25 32 42 45 36 39 37 34 41 38 Performance Rating 85 80 75 100 90 70 100 90 100 80 100 95 100 90 80 90 55 80 85 70 95 65 65 75 70 95 80 95 95 90 60 95 90 80 90 75 95 95 90 90 80 100 95 90 95 75 95 90 95 80 Service Gender Raise Degree Gender1 Gr 8 7 5 16 16 12 8 9 10 7 19 22 2 12 8 4 3 11 1 16 13 6 6 9 4 2 7 9 5 18 4 4 9 2 4 3 2 11 6 2 5 8 20 16 8 20 5 11 21 12 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1 0 0 5.7 3.9 3.6 5.5 5.7 4.5 5.7 5.8 4 4.7 4.8 4.5 4.7 6 4.9 5.7 3 5.6 4.6 4.8 6.3 3.8 3.3 3.8 4 6.2 3.9 4.4 5.4 4.3 3.9 5.6 5.5 4.9 5.3 4.3 6.2 4.5 5.5 6.3 4.3 5.7 5.5 5.2 5.2 3.9 5.5 5.3 6.6 4.6 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 M M F M M M F F M F F M F F F M F F M F M F F F M F M F M M F M M M F F F M F M M F F M F M M F M M E B B E D F C A F A A E C A A C E B A B F D A D A A C F F D A B E B A A A E B A C A F E D E E E E E The ongoing question that the weekly assignments will focu Note: to simplfy the analysis, we will assume that jobs with The column labels in the table mean: ID - Employee sample number Age - Age in years Service - Years of service (rounded) Midpoint - salary grade midpoint Grade - job/pay grade Gender1 (Male or Female) Salary - Salar Performance Gender - 0 = Raise - perce Degree (0= B Compa - salar us on is: Are males and females paid the same for equal work (under the Equal Pay Act)? hin each grade comprise equal work. ry in thousands Rating - Appraisal rating (employee evaluation score) male, 1 = female ent of last raise BS\\BA 1 = MS) ry divided by midpoint Score: <1 point> Week 5 Correlation and Regression 1. Create a correlation table for the variables in our data set. (Use analysis ToolPak or StatPlus:mac LE function Correlation.) a. Reviewing the data levels from week 1, what variables can be used in a Pearson's Correlation table (which is what Excel produces)? b. Place table here (C8): Salary Salary 1 Compa 0.56587 Midpoint 0.98526 Age 0.52769 Perf. 0.15246 Service 0.43938 Raise -0.03721 Compa Midpoint 1 0.42515 1 0.08949 0.56711 -0.10242 0.19175 0.13679 0.47115 -0.05529 -0.02891 Age 1 0.13924 0.56513 -0.18043 Perf. Service 1 0.2257 0.67366 1 0.10279 Raise 1 c. Using r = approximately .28 as the signicant r value (at p = 0.05) for a correlation between 50 values, what variables are significantly related to Salary? Age and service To compa? Age, midpoint and service d. Looking at the above correlations - both significant or not - are there any surprises -by that I mean any relationships you expected to be meaningful and are not and vice-versa? I didn't expect compa and age to be similar. Does this help us answer our equal pay for equal work question? This does not provide anymore clear cut information to our equal pay for equal work question. We do have significantly close variables, but there are varying degrees of data provided to make a clear conclusion. Below is a regression analysis for salary being predicted/explained by the other variables in our sample (Midpoint, age, performance rating, service, gender, and degree variables. (Note: since salary and compa are different ways of expressing an employee's salary, we do not want to have both used in the same regression.) Plase interpret the findings. e. <1 point> 2 Ho: The regression equation is not significant. Ha: The regression equation is significant. Ho: The regression coefficient for each variable is not significant Ha: The regression coefficient for each variable is significant Note: technically we have one for each input variable. Listing it this way to save space. Sal SUMMARY OUTPUT Regression Statistics Multiple R 0.99155907 R Square 0.9831894 Adjusted 0.98084373 Standard E 2.65759257 Observati 50 ANOVA df Regressio Residual Total SS MS F Significance F 6 17762.3 2960.383 419.15161 1.812E-036 43 303.70033 7.062798 49 18066 Standard Coefficients Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -1.74962121 3.6183677 -0.483539 0.6311665 -9.046755 5.54751262 -9.0467550427 5.547512618 Midpoint 1.21670105 0.0319024 38.13829 8.66E-035 1.15236383 1.28103827 1.1523638283 1.2810382727 Age -0.00462801 0.0651972 -0.070985 0.943739 -0.1361107 0.1268547 -0.1361107191 0.1268546987 Perf -0.05659644 0.0344951 -1.640711 0.1081532 -0.1261624 0.01296949 -0.1261623747 0.0129694936 Service -0.04250036 0.084337 -0.503935 0.6168794 -0.2125821 0.12758138 -0.2125820912 0.1275813765 Gender 2.420337212 0.8608443 2.811585 0.0073966 0.68427919 4.15639523 0.684279192 4.156395232 Degree 0.27553341 0.7998023 0.344502 0.7321481 -1.3374217 1.88848848 -1.3374216547 1.8884884833 Note: since Gender and Degree are expressed as 0 and 1, they are considered dummy variables and can be used in a multiple regression equation. Interpretation: For the Regression as a whole: What is the value of the F statistic: 419 What is the p-value associated with this value: 1.81E-036 Yes Is the p-value <0.05? Do you reject or not reject the null hypothesis: Reject What does this decision mean for our equal pay question: The regression equation is significant and pay is not equal and depends on all the factors provided within the data set For each of the coefficients: Intercept Midpoint Age Perf. Rat. Service Gender Degree What is the coefficient's p-value for each of the variables: 0.6311665 8.664E-035 0.94373899 0.1081531819 0.6168793519 0.007397 0.732148 Is the p-value < 0.05? No Yes No No No Yes No Do you reject or not reject each null hypothesis: No Yes No No No Yes No What are the coefficients for the significant variables? -1.7496212 1.21670105 -0.004628 -0.0565964405 -0.042500357 2.420337 0.275533 Using only the significant variables, what is the equation? Salary = 1.21670105*Midpoint + 2.42033721*Gender Is gender a significant factor in salary: Yes The employees with the highest midpoint. If so, who gets paid more with all other things being equal? How do we know? It is the only coefficient that is positive. <1 point> 3 Perform a regression analysis using compa as the dependent variable and the same independent variables as used in question 2. Show the result, and interpret your findings by answering the same questions. Note: be sure to include the appropriate hypothesis statements. Regression hypotheses Ho: The Compa regression analysis is not significant Ha: The compa regression analysis is significant Coefficient hyhpotheses (one to stand for all the separate variables) Ho: Ha: Place D94 in output box. Regression Statistics R 0.96277 R-square 0.92692 Adjusted R 0.91474 S 0.02312 N 50 ANOVA d.f. SS MS F p-level Regression 7 0.28471 0.04067 76.09877 Residual 42 0.02245 0.00053 Total 49 0.30716 0 Coefficient Standard Erro LCL UCL t Stat p-level H0 (5%) Intercept 1.06026 0.03191 0.99585 1.12466 33.22167 0 rejected Salary 0.02083 0.00124 0.01833 0.02334 16.7932 0 rejected Midpoint -0.02208 0.00155 -0.02521 -0.01895 -14.22585 0 rejected Age -0.00034 0.00055 -0.00145 0.00077 -0.61487 0.54196 accepted Perf. Ratin -0.00011 0.00031 -0.00073 0.00051 -0.36199 0.71918 accepted Service 0.00134 0.00074 -0.00016 0.00284 1.80643 0.07802 accepted Gender 0.00281 0.0087 -0.01475 0.02037 0.32318 0.74816 accepted Degree -0.00719 0.00662 -0.02056 0.00618 -1.0856 0.28385 accepted Interpretation: For the Regression as a whole: What is the value of the F statistic: 76 0 What is the p-value associated with this value: No Is the p-value < 0.05? Do you reject or not reject the null hypothesis: Rejected What does this decision mean for our equal pay question: For each of the coefficients: Intercept Midpoint Age Perf. Rat. Service What is the coefficient's p-value for each of the variables: 0 0 0.54196 0.71918 0.07802 Is the p-value < 0.05? No No Yes Yes Yes Do you reject or not reject each null hypothesis: Reject Reject Not Rej. Not Rej. Not Rej. What are the coefficients for the significant variables? 1.06026 -0.02208 -0.00034 -0.00011 0.00134 Using only the significant variables, what is the equation? Compa = .00281*Gender + .00134*Service Is gender a significant factor in compa: Yes If so, who gets paid more with all other things being equal? Those with higher service factors How do we know? It's the other significant value in the equation <1 point> 4 <2 points> 5 Gender 0.74816 Yes Not Rej. 0.00281 Degree 0.28385 Yes Not Rej. -0.00719 Based on all of your results to date, Do we have an answer to the question of are males and females paid equally for equal work? If so, which gender gets paid more? How do we know? Which is the best variable to use in analyzing pay practices - salary or compa? Why? What is most interesting or surprising about the results we got doing the analysis during the last 5 weeks? Why did the single factor tests and analysis (such as t and single factor ANOVA tests on salary equality) not provide a complete answer to our salar What outcomes in your life or work might benefit from a multiple regression examination rather than a simpler one variable test? ry equality question? Regression Statistics R 0.96277 R-square 0.92692 Adjusted R 0.91474 S 0.02312 N 50 ANOVA d.f. SS MS F p-level Regression 7 0.28471 0.04067 76.09877 Residual 42 0.02245 0.00053 Total 49 0.30716 0 Coefficient Standard Er LCL UCL t Stat p-level H0 (5%) Intercept 1.06026 0.03191 0.99585 1.12466 33.22167 0 rejected Salary 0.02083 0.00124 0.01833 0.02334 16.7932 0 rejected Midpoint -0.02208 0.00155 -0.02521 -0.01895 -14.22585 0 rejected Age -0.00034 0.00055 -0.00145 0.00077 -0.61487 0.54196 accepted Perf. Rating -0.00011 0.00031 -0.00073 0.00051 -0.36199 0.71918 accepted Service 0.00134 0.00074 -0.00016 0.00284 1.80643 0.07802 accepted Gender 0.00281 0.0087 -0.01475 0.02037 0.32318 0.74816 accepted Degree -0.00719 0.00662 -0.02056 0.00618 -1.0856 0.28385 accepted Standard Coefficients Error Intercept -1.74962 3.618368 Midpoint 1.216701 0.031902 Age -0.00463 0.065197 Perf -0.0566 0.034495 Service -0.0425 0.084337 Gender 2.420337 0.860844 Degree 0.275533 0.799802 t Stat -0.48354 38.13829 -0.07098 -1.64071 -0.50394 2.811585 0.344502 P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 0.631166 -9.04676 5.547513 -9.04676 5.547513 9E-035 1.152364 1.281038 1.152364 1.281038 0.943739 -0.13611 0.126855 -0.13611 0.126855 0.108153 -0.12616 0.012969 -0.12616 0.012969 0.616879 -0.21258 0.127581 -0.21258 0.127581 0.007397 0.684279 4.156395 0.684279 4.156395 0.732148 -1.33742 1.888488 -1.33742 1.888488