Assignment 11

Example Assignment Eleven: Using multiple regression to analyze the gender pay gap Part I: Use APA style and formatting for all assignments, references, and citations. Yes, have a cover page, too, as well as a running head. Try Purdue Owl for an example APA style paper: https://owl.english.purdue.edu/owl/resource/560/18/ For this final analysis you get to bring together many of the variables we have been using this term to better understand difference in income. In particular we want to explain the gender pay gap between women and men. For Ordinary Least Squares (OLS) regression analyses, which we are using for this assignment, you want to have at least one interval/ratio independent variable and an interval/ratio dependent variable. Your dependent variable is pincp. Your independent variables will be sex, agep, and schl. But, there are other variables that might explain variation in income. For this analysis we will add race to our independent variable list. However, as your book tells you, for the nominal variables we need to do a little recoding into “dummy” variables so we can use OLS regression more effectively. We will recode sex into a dummy variable called “Male.” And, we will recode rac1p into a dummy variable called “White.” Also, know that there are more tests that need to be done to come to firmer conclusions from an OLS analysis. For example, two independent variables might also have a strong association where one predicts the other to a large degree. Might this be the case for sex and schl? When this happens it is known as multicollinearity or just collinearity and it can impact OLS regression results. There are ways to test for it and correct the problem, but we are not going to do that in this course. Just know that there is more to OLS regression than what you practice here. You are practicing running and interpreting the analysis. 1. What is the measure (nominal, ordinal, or interval/ratio) of each of your independent variables and your dependent variable? Dependent variable, pincp: I/R Independent variable, rac1p: Nominal Independent variable, sex: Nominal Independent variable, agep: I/R Independent variable, schl: I/R I answer for you because I want you to treat this as an I/R variable for years of schooling even though it is not exactly year for year the years of schooling. You can check the data dictionary for schl to see how the answers are coded. They are coded from 1 to 16 where each number means progressively more education. 2. Using your 2014-2018 ACS data file, recode your nominal independent variables as instructed in the text under 17.2 Recoding to Create Dummy Variables and from past assignments to transform each nominal variable, sex and rac1p, into a new variable. 3. For sex code Male=1 and Female = 0 in a new variable Male. Male is already coded 1, but you need to make 1 = 1 in the new variable anyway. Female is coded as 2, so you have to change the 2 to a 0. The new variable, male, should be numeric when you are done. Here is a screen shot to help you:

4. Next assign labels to the values for your new variable, male. So, 1=Male and 0=Female. We have done assigned labels before. See screen shot below to help guide you. 5. Save your file with the new variable, male. 6. For rac1p code white=1 and nonwhite = 0 in a new variable white. Recoding rac1p is a little more complicated to recode thnt sex was because it has many values-white, black, native, etc. If

8. Save your file with the new variable, white. 9. Congratulations, you have just created your first dummy variables. You can now use these recoded variables in a regression analysis and treat them as interval/ratio variables, known as dummy variables. 10. Follow the directions in your text for demonstration 17.3, which begins on page 324, entitled “Multiple Regression.” Use your new variables male and white in addition to agep and schl. So four total independent variables. You should know your dependent variable. 11. Copy and paste your output table that look like the “Model Summary,” table in your text on page 324. Here is where this is going to get fun for you to see the numbers. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .416a .173 .173 72246.727 a. Predictors: (Constant), SCHL, AGEP, White, Male 12. Remember R? What is R for our model? R = 0.416 13. Using your text in past chapters to guide you, how strong (or not) is the correlation (R) between the independent variables and the dependent variable? Hint: This answer is not a number but is based on a number. Correlation strength = moderate

14. Remember our friend R-square that tells us how much of the variation in, in this case, income, is explained by the independent variables, in this case male, agep, schl, and white? What is R- square for this full model? R-square = 0.173 15. How much of the variation in income is accounted for using male, agep, schl, and white? Hint: this number is a percent. Explained variation in income = 17.3% 16. In a perfect model that predicts 100 percent of the variation in income, R-square =100 percent or 1.00. So, now think about this, if this model predicts income at the percent you gave in number 14, how much of the variation in income is still unaccounted for? Hint: this number is a percent and you have to use subtraction. 100% - R-square = 100% - 17.3% = 82.7% Unaccounted for variation = 82.7% 17. Copy and paste your table that looks like the one on page 325 entitled “Coefficients.” Now you get to use the equation you practiced in a past assignment for one independent variable, but instead now for many independent variables used to predict income. This is the equation for the model. Coefficients a Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) -127344.606 124.980 -1018.922 .000 Male 21983.308 41.675 .136 527.493 .000 White 9245.157 41.821 .057 221.063 .000 AGEP 1348.528 1.604 .216 840.529 .000 SCHL 6742.781 5.170 .337 1304.091 .000 a. Dependent Variable: PINCP 18. Using this equation: Ŷ = a + b X 1 + b X 2 + b X 3 + b X 4 from your text, fill in the values for the constant, and the Beta values for each independent variable. Do you notice how there is a “b” in the equation for each independent variable? If you had five independent variables you would have one more b X term in your equation. 19. Write out and solve the equation for a 25-year-old, white, male with 12 years of education. Ŷ = -127344.606 + 21983.308(25) + 9245.157(1) + 1348.528(1) + 6742.781(12) Ŷ = -127344.606 + 549582.7 + 9245.157 + 1348.528 + 80913.372 Ŷ = 446745.151 20. Write a concluding statement about the income of your results in number 19. Use a full sentence. The predicted income for a 25-year-old, white, male with 12 years of education is approximately $446,745.15. This value comes from the combination of age, race, gender, and education level indicated by the coefficients in the model.

Age = 0.000 Education = 0.000 White =0.000 30. Are your independent variables significant to p<.05 level? Yes, all the independent variables in the model which are Male, White, Age, and Education are statistically significant to the p < .05 level. 31. What does significance mean? Offer sentences that concludes the significance levels and what they mean in interpreting your results. In the model all the independent variables Male, White, Age, and Education have p-values less than 0.05. The probability of the observed relationships between these variables and income occurring by random chance is very low. Based on the evidence we can suggest that being male, being white, increasing age, and higher levels of education are associated with statistically significant changes in income. 32. We know there is a gender pay gap in the U.S. and in California. Given what you know from your analyses here, what would you say about income, gender, and what people earn in California for full-time, year-round work? Use as much information from this analysis and past analyses as you think relevant to discuss the gender pay-gap in California for full-time year-round workers. According to the analysis there is a statistically significant difference between the expected incomes of men and women for full-time, year-round workers in California, with men generally earning higher incomes. The coefficient for the variable "Male" is positive 21983.308, indicating that on average, males tend to have higher predicted incomes compared to females when other variables are held constant. It's important to consider the complexity of the gender pay gap, considering social and practical factors that also contribute to the gender pay gap.