OPTION A: Gender and Racial differences in payments in federal jobs Mr. Cartwright is the director of the Office of Personnel and Management (OPM). One employee recently complained to him that even in Federal jobs there exist unexplained salary differences between male and female employees and employees of different racial background. Mr. Cartwright is of the opinion that educational and other 'quality' measures are reasons of such differences and there is no gender or race bias in the federal salaries. He has asked you, the brilliant analysts from MGS 3100 to create a regression model to prove or disprove his claim. He has supplied you with the dataset salary_federal.xls which contains the salary and other information about some randomly sampled federal employees whose names are withheld for reasons of anonymity and to protect their privacy. Your task is to create a regression model that contains at least FIVE (more would be better, but five is the minimum necessary) explanatory variables (that explain/predict) salary of these employees. From this regression model you have to conclude whether you have found any evidence to support the claim of gender and 2 racial discrimination in federal payment structure or not. Description of the dataset is provided at the end of this document. What you need to do in your project as part of the data analysis (whether you choose Option A or Option B) 1. Show descriptive statistics of all the variables. [to get some feel for the data]. Descriptive statistics are average or mean, standard deviation, maximum, minimum, etc. 3 2. Show relationships of each independent variable individually with the dependent variable using scatter plots. Remember to correctly label the horizontal and vertical axes in each diagram. [this is to get some initial feeling about which variables are more related to the dependent variables, and look for possible outliers or influence points] (In Excel: Insert - Charts - Scatter) 3. Perform regression analysis to show overall model for predicting the value of the dependent variable. (You might need to activate the Analysis toolpack Excel plug-in/addin in your Excel. Once you have done that regression can be run by Data - Analysis - Regression). But as we discussed in class, the first model that you estimate is most likely not be your final model. You will need to drop (sometimes add as well) bad variables from the model and reestimate the model again. This is a crucial step. Do not ask me how many times you should reestimate or how many models should be there - there is no answer to that. What I want to see indication of the fact that you have understood the idea of how regression analysis is done through trial and error of including and dropping of variables. So start with a handful (much more than 5) of variables that can be expected to affect your dependent variable. Then drop the ones that does not seem good after you do your initial regression or regressions. This is an iterative process and will take both time and patience. We can talk more about this step during office hour. 4. Interpret the results and write a report using those interpretations that conforms to the sample memo format. Submittals: Report - Single spaced one or two pages Word document (do not embed in Excel) that conforms to the sample memo format and contains: Introduction should contain 1. Why you are interested in the topic: the background of your project 2. What you are trying to predict - your dependent variable. 3. Why you choose certain independent variables for your project. Why do you think those independent or explanatory variables are going to affect the dependent of explained variable? [Logical explanation is required.] 4. How you collected the data (e.g., survey or from Web or from some book) [You should clearly write the source of the data.] Analysis [do not insert any graph or diagram] 4 5. Findings from descriptive statistics and scatter plot [It does not have to be thorough; write what variables are expected to have relationship with the dependent variable.] 6. List of insignificant independent variables in a full model (i.e., a model with all the independent variables) 7. Order of the dropped independent variables in a subsequent regression analyses with reasoning of such order 8. Equation of the final model (i.e., a model with only significant independent variable(s)) 9. Performance of the final model. i.e., how good your model is? Look at your F-significance number and R-squared value for answering this. [Low R-squared does not mean low grade.] 10. Findings from the final model. i.e., interpretation of the coefficients of the independent variables [Make sure that all the coefficients make sense. If it does not, explain further how such odd coefficient can be justified] Excel file Your excel file should have raw data and outputs of all the regression analyses you did. Each worksheet should be clearly named "raw data," "scatter plot," "regression 1, (Full Model)" "regression 2," and so on... finishing with \"Final Regression\". But note that I am not saying you will run three regressions only (Full Model, Regression 2, and final model). You may need more depending on the iterative process that I discussed in point 3 above. [Example] Your report should be written clearly about what you want to do in the project, what you have found, and how you have found. Your report should be easy to read and understand without referring to your Excel file. sal grade 55250 74765 95469 51235 55203 62102 85249 39719 31262 49850 34662 39009 56605 63399 76814 46103 65619 34662 116529 47013 45064 49002 64928 59756 44802 45063 68111 65026 34375 67880 66894 73391 74054 30557 28622 65235 56101 41543 74741 47081 38734 52619 54941 36313 36085 42928 48304 36123 61479 35818 51612 68294 30557 63263 68108 76733 51801 48466 32466 64926 54340 75532 111839 57280 54340 41596 44972 83926 45063 58026 48356 47873 58270 60378 50541 51612 75289 79509 50774 56576 67135 71352 42366 28101 62958 41596 47013 75894 49345 45116 76733 51419 54941 34755 51612 12 14 15 12 13 13 15 11 9 12 11 11 13 14 14 11 13 11 16 12 12 12 13 13 12 11 14 14 9 14 14 14 15 9 7 14 13 12 14 12 11 12 13 11 11 12 12 9 13 11 13 14 9 13 14 14 12 12 9 14 13 15 16 13 13 11 12 15 11 12 12 12 13 13 13 13 14 14 12 12 14 14 11 7 14 11 12 14 12 12 14 12 13 9 13 patco age professional professional professional 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