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): c. d. 2 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. <1 point> 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? To compa? Does this help us answer our equal pay for equal work question? 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. 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 R Square 0.98084373 Standard Error 2.65759257 Observations 50 ANOVA df Regression 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 Performace Rating -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: 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? Midpoint Age Perf. Rat. Service Gender Degree Using only the significant variables, what is the equation? Is gender a significant factor in salary: If so, who gets paid more with all other things being equal? How do we know? <1 point> 3 Salary = 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: 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? Using only the significant variables, what is the equation? Compa = Is gender a significant factor in compa: If so, who gets paid more with all other things being equal? How do we know? <1 point> 4 <2 points> 5 Midpoint Age Perf. Rat. Service Gender Degree 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 sala What outcomes in your life or work might benefit from a multiple regression examination rather than a simpler one variable test? ary equality question? See comments at the right of the data set. ID Salary Compa Midpoint Age 8 10 11 14 15 23 26 31 35 36 37 42 3 18 20 39 7 13 22 24 45 17 48 28 43 19 25 40 2 32 34 16 27 41 5 30 1 4 12 33 38 44 46 47 49 50 6 9 21 29 23 22 23 24 24 23 24 24 24 23 22 24 34 36 34 35 41 42 57 50 55 69 65 75 77 24 24 25 27 28 28 47 40 43 47 49 58 66 60 64 56 60 65 62 60 66 76 77 76 72 1.000 0.956 1.000 1.043 1.043 1.000 1.043 1.043 1.043 1.000 0.956 1.043 1.096 1.161 1.096 1.129 1.025 1.050 1.187 1.041 1.145 1.210 1.140 1.119 1.149 1.043 1.043 1.086 0.870 0.903 0.903 1.175 1.000 1.075 0.979 1.020 1.017 1.157 1.052 1.122 0.982 1.052 1.140 1.087 1.052 1.157 1.134 1.149 1.134 1.074 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 57 67 67 67 67 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 38 36 49 43 52 Performance Service Gender Raise Degree Gender1 Grade Rating 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 80 70 100 95 95 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 12 12 10 13 5 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 0 0 0 0 0 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 4.6 4.5 4 6.3 5.4 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 1 0 F F F F F F F F F F F F F F F F F F F F F F F F F M M M M M M M M M M M M M M M M M M M M M M M M M A A A A A A A A A A A A B B B B C C D D D E E F F A A A B B B C C C D D E E E E E E E E E E F F F F The ongoing question that the weekly assignments wi Note: to simplfy the analysis, we will assume that jobs 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 - S Performan Gender: 0 Raise - pe Degree (0= Compa - s will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)? s within each grade comprise equal work. Salary in thousands nce Rating - Appraisal rating (Employee evaluation score) 0 = male, 1 = female ercent of last raise = BS\\BA 1 = MS) salary divided by midpoint