The Glass Ceiling: A Study on Annual SalariesAgendaIntroductionSlide 4Exploratory AnalysisSlide 6Slide 7Slide 8Slide 9Slide 10Slide 11Linear Regression & AnalysisSlide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20ConclusionFurther AnalysisFinThe Glass Ceiling: A Study The Glass Ceiling: A Study on Annual Salarieson Annual SalariesGroup 4Group 4Julie Shan, Brian Abe, Yu-Ting Cheng, Kathinka Tysnes, Huan Julie Shan, Brian Abe, Yu-Ting Cheng, Kathinka Tysnes, Huan Zhang, Andrew BoothZhang, Andrew BoothAgendaAgendaIntroductionIntroductionExploratory AnalysisExploratory AnalysisLinear Regression & AnalysisLinear Regression & AnalysisConclusionConclusionFurther AnalysisFurther AnalysisIntroductionIntroductionWhat?What?A sample of 1980’s managers A sample of 1980’s managers salariessalariesWhy?Why?To determine factors that affect the To determine factors that affect the salarysalaryHow?How?Linear regressionLinear regressionIntroductionIntroductionData Set AnalyzedData Set AnalyzedA subsample of a large data set (from the A subsample of a large data set (from the early 1980s) from a study investigating early 1980s) from a study investigating potential gender bias in determination of potential gender bias in determination of professional salary differentials. The professional salary differentials. The individuals come from several large individuals come from several large corporations. corporations. Data was organized byData was organized byManagement LevelManagement LevelGenderGenderEducation LevelEducation LevelYears in JobYears in JobSalarySalaryExploratory AnalysisExploratory AnalysisExploratory AnalysisExploratory AnalysisAffects of the independent Affects of the independent variables on the dependent variables on the dependent variable SALARY.variable SALARY.Independent Variables:Independent Variables:Years in jobYears in jobManagement levelManagement levelEducation levelEducation levelGenderGenderExploratory AnalysisExploratory AnalysisPositive Positive Relationship Relationship Between Years Between Years in Job and in Job and SalarySalary10000150002000025000300000 4 8 12 16 20 24YEARSSALARYSalary vs. Years in JobExploratory AnalysisExploratory AnalysisUpper Upper Management Management Earns More Earns More Than Lower Than Lower ManagementManagement1000015000200002500030000-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2MANAGEMENTSALARYSalary vs. Management LevelExploratory AnalysisExploratory AnalysisMore More Educated Educated Managers Managers Earn MoreEarn MoreOutliers May Outliers May Skew Skew Regression Regression ResultsResults10000150002000025000300000 1 2 3 4EDUCATIONSALARYSalary vs. Education LevelExploratory AnalysisExploratory AnalysisFemale=0 if Female=0 if MaleMaleFemale=1 if Female=1 if FemaleFemaleNote: Many Note: Many More Males More Males than Females than Females in Data Setin Data SetFemales Seem Females Seem to have Cap, to have Cap, Lower Max Lower Max SalarySalary1000015000200002500030000-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2FEMALESALARYSalary vs. FemaleExploratory AnalysisExploratory AnalysisNew Variable: Female_managementNew Variable: Female_management1 and 2 correspond to men and women in lower management 1 and 2 correspond to men and women in lower management respectivelyrespectively3 and 4 correspond to men and women in upper management 3 and 4 correspond to men and women in upper management respectivelyrespectivelyAgain, females earn less, have a cap on salaryAgain, females earn less, have a cap on salary10000150002000025000300000 1 2 3 4 5FEMALE_MANAGEMENTSALARYSalary vs. Female_ManagementLinear Regression & Analysis Linear Regression & Analysis A regression of A regression of salary vs. the salary vs. the other variablesother variablesEd1-3 are Ed1-3 are dummy dummy variables for variables for education leveleducation levelEd1=high schoolEd1=high schoolEd2=bachelorsEd2=bachelorsEd3=graduate Ed3=graduate degreedegreeLinear Regression & Analysis Linear Regression & Analysis All variables, except female, are All variables, except female, are significant at a 5% level.significant at a 5% level.RR22 = 0.94, so it is a good fit = 0.94, so it is a good fitThe Durbin-Watson is less than 2 The Durbin-Watson is less than 2 but greater than 1.but greater than 1.Linear Regression & Analysis Linear Regression & Analysis Jarque-Bera statistic is greater than Jarque-Bera statistic is greater than 0.05, indicating normality of the 0.05, indicating normality of the residualsresiduals0246810-2000 -1000 0 1000 2000 3000Series: ResidualsSample 1 43Observations 43Mean -1.45e-12Median 6.465925Maximum 3085.931Minimum -2363.230Std. Dev. 1280.438Skewness 0.299525Kurtosis 2.570329Jarque-Bera 0.973732Probability 0.614549Histogram of ResidualsLinear Regression & Analysis Linear Regression & Analysis Updated regression excluding Updated regression excluding variable FEMALE.variable FEMALE.Linear Regression & Analysis Linear Regression & Analysis RR22 = 0.93: still a good fit. = 0.93: still a good fit.The Durbin-Watson statistic is The Durbin-Watson statistic is once again less than 2 but once again less than 2 but greater than 1greater than 1Linear Regression & Analysis Linear Regression & Analysis Jarque-Bera statistic is greater than Jarque-Bera statistic is greater than 0.05, indicating normality of the 0.05, indicating normality of the residualsresiduals012345678-3000 -2000 -1000 0 1000 2000 3000Series: ResidualsSample 1 43Observations 43Mean -2.44e-12Median -148.6636Maximum 2850.258Minimum -2681.484Std. Dev. 1338.158Skewness 0.193549Kurtosis 2.286455Jarque-Bera 1.180694Probability 0.554135Histogram of ResidualsLinear Regression & Analysis Linear Regression & Analysis Wald Test for equivalency of Wald Test for equivalency of intercepts for various education intercepts for various education levelslevelsHHo o : ED2=ED3: ED2=ED3HHo o : ED1=ED2: ED1=ED2Linear Regression & Analysis Linear Regression & Analysis Final Model:Final Model:SALARY = 615.0378*YEARS + SALARY = 615.0378*YEARS + 7509.9807*MANAGEMENT + 7509.9807*MANAGEMENT + 7352.3861*ED1 + 7352.3861*ED1 + 10907.4441*ED2310907.4441*ED23Linear Regression & Analysis Linear Regression & AnalysisConclusionConclusionThe variable FEMALE was not
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