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 66.6 26.4 35.3 56 47.5 75.5 41.5 22.8 74 24.1 23.6 63.4 41.4 23 23.6 44.1 63.7 35.9 24 33.6 74.8 52.1 22.9 51.7 24.8 24.3 41.4 75.2 72.8 47.4 22.7 27.5 59.3 28.5 24.1 24.6 23.6 62.7 1.168 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 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 0.851 1.140 0.983 0.990 1.127 1.037 0.990 1.104 1.046 1.026 1.113 1.035 1.001 1.024 1.102 1.118 1.158 1.045 1.084 1.117 1.085 0.996 1.078 1.080 1.057 1.035 1.122 1.086 0.987 0.986 0.886 1.040 0.918 1.047 1.069 1.027 1.100 Performance Service Gender Raise 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 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 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 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 39 40 41 42 43 44 45 46 47 48 49 50 36.1 24.4 44.7 22.4 76.7 66.3 52.8 62.5 55.1 70.8 61.7 57.3 1.164 1.059 1.117 0.975 1.145 1.163 1.101 1.096 0.967 1.242 1.083 1.006 31 23 40 23 67 57 48 57 57 57 57 57 27 24 25 32 42 45 36 39 37 34 41 38 90 90 80 100 95 90 95 75 95 90 95 80 6 2 5 8 20 16 8 20 5 11 21 12 1 0 0 1 1 0 1 0 0 1 0 0 5.5 6.3 4.3 5.7 5.5 5.2 5.2 3.9 5.5 5.3 6.6 4.6 Degree Gender 1 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 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 Gr 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 The ongoing question that the weekly assignments will focus on is: Are males and fema Note: to simplfy the analysis, we will assume that jobs within each grade comprise equa The column labels in the table mean: ID - Employee sample number Salary - Salary in thousands Age - Age in years Performance Rating - Appraisal rating (emp Service - Years of service (rounded) Gender - 0 = male, 1 = female Midpoint - salary grade midpoint Raise - percent of last raise Grade - job/pay grade Degree (0= BS\\BA 1 = MS) Gender1 (Male or Female) Compa - salary divided by midpoint 0 0 0 1 0 1 1 1 1 1 0 0 F M M F F M F M M F M M B A C A F E D E E E E E on is: Are males and females paid the same for equal work (under the Equal Pay Act)? each grade comprise equal work. thousands g - Appraisal rating (employee evaluation score) , 1 = female vided by midpoint Sal Compa 24 1.045 24.2 1.053 23.4 1.018 23.4 1.017 22.6 0.983 22.9 0.995 23.1 1.003 23.3 1.011 22.7 0.985 23.5 1.023 23 1.002 24 1.042 35.5 1.145 34.7 1.119 35.5 1.146 35.2 1.136 40.4 1.01 42.7 1.068 53.4 1.112 51.5 1.072 49.8 1.037 68.3 1.198 65.4 1.148 78.4 1.17 75.9 1.133 24 1.044 23.3 1.012 24.1 1.049 27.5 0.887 27.1 0.875 27.7 0.895 40.8 1.019 43.9 1.097 41 1.025 48.7 1.014 49.4 1.029 64.4 1.13 64.5 1.132 58.9 1.033 57.9 1.016 59 1.035 63.3 1.111 56.8 0.996 58 1.017 62.4 1.094 G 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Mid 23 23 23 23 23 23 23 23 23 23 23 23 31 31 31 31 40 40 48 48 48 57 57 67 67 23 23 23 31 31 31 40 40 40 48 48 57 57 57 57 57 57 57 57 57 Age 32 30 41 32 32 36 22 29 23 27 22 32 30 31 44 27 32 30 48 30 36 27 34 44 42 32 41 24 52 25 26 44 35 25 36 45 34 42 52 35 45 45 39 37 41 EES 90 80 100 90 80 65 95 60 90 75 95 100 75 80 70 90 100 100 65 75 95 55 90 95 95 85 70 90 80 95 80 90 80 80 90 90 85 100 95 90 95 90 75 95 95 SR 9 7 19 12 8 6 2 4 4 3 2 8 5 11 16 6 8 2 6 9 8 3 11 9 20 1 4 2 7 4 2 4 7 5 16 18 8 16 22 9 11 16 20 5 21 G 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Raise 5.8 4.7 4.8 6 4.9 3.3 6.2 3.9 5.3 4.3 6.2 5.7 3.6 5.6 4.8 5.5 5.7 4.7 3.8 3.8 5.2 3 5.3 4.4 5.5 4.6 4 6.3 3.9 5.6 4.9 5.7 3.9 4.3 5.7 4.3 5.7 5.5 4.5 5.5 4.5 5.2 3.9 5.5 6.6 Deg 1 1 1 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 63.8 1.12 79 1.179 77 1.149 74.8 1.116 76 1.135 0 0 0 0 0 57 67 67 67 67 38 36 49 43 52 80 70 100 95 95 12 12 10 13 5 0 0 0 0 0 4.6 4.5 4 6.3 5.4 0 1 1 1 0 SUMMARY OUTPUT Regression Statistics Multiple R 0.705018 R Square 0.49705 Adjusted R 0.413225 Standard E 0.056125 Observatio 50 ANOVA df Regression SS 7 MS Significance F 0.13075 0.018679 5.929623 7.83E-005 Residual 42 0.132302 Total 49 0.263052 0.00315 Coefficients Standard Error t Stat Intercept F P-value Lower 95%Upper 95% Lower 95.0% Upper 95.0% 0.948624 0.081717 11.60868 1.09E-014 0.783713 1.113535 0.783713 1.113535 Mid 0.0035 0.000649 5.390013 2.98E-006 0.002189 0.00481 0.002189 0.00481 Age 0.000553 0.001446 0.382293 0.704172 -0.002365 0.003471 -0.002365 0.003471 EES -0.001846 0.001025 -1.800846 0.078911 -0.003915 0.000223 -0.003915 0.000223 SR -0.000418 0.001828 -0.228814 0.820124 -0.004107 0.00327 -0.004107 0.00327 G 0.064665 0.01834 3.525963 0.001035 0.027654 0.101676 0.027654 0.101676 Raise 0.014655 0.013909 1.053639 0.298072 -0.013414 0.042724 -0.013414 0.042724 Deg 0.001468 0.01611 0.0911 0.927847 -0.031043 0.033979 -0.031043 0.033979 t-Test: Two-Sample Assuming Equal Variances Variable 1 Variable 2 Mean Variance Observatio 1.06684 0.004302 0.006481 25 Pooled Var 0.005391 Hypothesiz df t Stat 1.04836 0 48 0.889835 P(T<=t) one0.188996 t Critical on 1.677224 P(T<=t) two0.377993 t Critical tw 2.010635 25 SUMMARY OUTPUT Regression Statistics Multiple R 0.993129 R Square 0.986305 Adjusted R 0.984022 Standard E 2.435282 Observatio 50 ANOVA df Regression SS 42 249.0852 Total 49 18187.51 Significance F 5.9306 Coefficients Standard Error t Stat Intercept F 7 17938.42 2562.632 432.1034 5.30E-037 Residual Upper 95.0% MS -4.871454 3.545701 -1.373905 P-value Lower 95%Upper 95% Lower 95.0% Upper 95.0% 0.17676 -12.02697 2.284059 -12.02697 2.284059 Mid 1.228416 0.028171 43.60516 1.32E-036 1.171563 1.285268 1.171563 1.285268 Age 0.036828 0.06274 0.586996 0.560349 -0.089786 0.163442 -0.089786 0.163442 EES -0.082158 0.044484 -1.846901 0.071815 -0.171931 0.007615 -0.171931 0.007615 SR -0.077848 0.079309 -0.981585 0.331925 -0.2379 0.082203 -0.2379 0.082203 G 2.914508 0.795761 3.662545 0.000694 1.308599 4.520418 1.308599 4.520418 Raise 0.676329 0.603509 1.120662 0.268799 -0.541601 1.894259 -0.541601 1.894259 Deg 0.034504 0.699007 0.049362 0.960865 -1.376149 1.445158 -1.376149 1.445158 Upper 95.0% 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): c. Using r = approximately .28 as the significant r value (at p = 0.05) for a correlation between 50 values, what variables are significantly related to Salary? To compa? 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? e. Does this help us answer our equal pay for equal work question? 2. 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.) Please interpret the findings. Note: These values are not the same as the data the assignment uses. The purpose is to analyze the result of a regression test rather than directly answer our equal pay question. Ho: The regression equation is not significant. Ha: The regression equation is significant. Ho: The regression coefficient for each variable is not significant Note: technically we have one for each input variable. Ha: The regression coefficient for each variable is significant. Listing it this way to save space. Sal SUMMARY OUTPUT Regression Statistics Multiple R 0.9915591 R Square 0.9831894 Adjusted R Square 0.9808437 Standard Error 2.6575926 Observations 50 ANOVA Regression Residual Total df 6 43 49 SS 17762.3 303.7003 18066 MS 2960.38 7.0628 F Significance F 419.1516 1.812E-36 Coefficients Coefficients Standard Error Intercept Midpoint Age Performace Rating Service Gender -1.7496 1.2167 -0.0046 -0.0566 -0.0425 2.42034 3.61837 0.0319 0.0652 0.0345 0.08434 0.86084 -0.4835 38.1383 -0.071 -1.6407 -0.5039 2.81159 Degree 0.27553 0.7998 0.3445 t Stat Lower 95% Upper 95% Lower 95.0% Upper 95.0% 0.631166 8.66E-35 0.943739 0.108153 0.616879 0.007397 -9.0468 1.15236 -0.1361 -0.1262 -0.2126 0.68428 5.54751 1.28104 0.12685 0.01297 0.12758 4.1564 -9.0468 1.15236 -0.1361 -0.1262 -0.2126 0.68428 5.54751 1.28104 0.12685 0.01297 0.12758 4.1564 0.732148 -1.3374 1.88849 -1.3374 1.88849 P-value 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: What is the p-value associated with this value: Is the p-value <0.05? Do you reject or not reject the null hypothesis: 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: Intercept 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? Salary = Is gender a significant factor in salary: If so, who gets paid more with all things being equal? How do we know? Midpoint Age Perf. Rat. Service Gender Degree NA NA NA 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 c94 in output box. Using the intercept coefficient and only the significant variables, what is the equation? 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: Intercept 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? Compa = Is gender a significant factor in compa: How do we know? Midpoint Age Perf. Rat. Service Gender Degree NA NA NA 4. Based on all your results to date, Do we have an answer to the question of are males and females paid equally for equal work? Does the company pay employees equally for for equal work? 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? 5. 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 salary equality question? What outcomes in your life or work might benefit from a multiple regression examination rather than a simpler one variable test? Regardless of statistical significance, who gets paid more with all other things being? Using the intercept coefficient and only the significant variables, what is the equation? Note: These values are not the same as in the data the assignment uses. The purpose is to analyze the result of a 2-way ANOVA test rather than directly answer our equal pay