Homework Assignment 4

Does higher proportion of women graduates within a major predict a lower or higher median income?

The dataset used for this regression analysis is taken from data.world. The dataset is data taken from American Community Survey 2010-2012 Public Use Microdata Series to help understand earnings between college majors and various variables.For the purpose of this assignment, the dependent variable (Y) for this regression is median income and the independent variable(X) is the proportion of gradautes who are women. The question we will be studying is does higher proportion of women graduates (via using Sharewomen variable) within a major predict a lower or higher median income.

Loading Packages

library(readr)
library(dplyr)
library(texreg)
library(ggplot2)

Importing and viewing Data Set

recent_grads <- read_csv("/Users/Deepakie/Documents/Queens College/SOC712/Data/recent-grads.csv")
head(recent_grads)
tail(recent_grads)

Selecting variables to keep * Major * College Major Category * Share Women * Unemployement Rate * Median Earnings

recent_grads <- select (recent_grads,
                         Major,Major_category,ShareWomen, Unemployment_rate, Median)

Renaming Variables

recent_grads <- rename(recent_grads, 
       "CollegeMajor" = Major,
       "CollegeMajorCategory"= Major_category,
       "UnemploymentRate" = Unemployment_rate, 
       "MedianEarnings" = Median)

Looking at Edited Data

print(recent_grads)

Descriptive Analysis

ggplot(data = recent_grads) + 
  geom_point(mapping = aes(x = ShareWomen, y = MedianEarnings)) +
  geom_smooth(mapping = aes(x = ShareWomen, y = MedianEarnings)) 

We see in the above graph, that the higher percentage of graduated women there are, the lower the median earnings are. For example, lets say the share proportion of women for a major is .50, meaning 50% graduates in that major were women; the median income would be 50% lower than it would be if a major had share proportion of women of 0%. Lets run a regression model and see our results.

Simple Linear Regression

The relationship between Median Income and Share of Women

Regressionmodel <- lm(MedianEarnings ~ ShareWomen, data=recent_grads)
summary(Regressionmodel)

Call:
lm(formula = MedianEarnings ~ ShareWomen, data = recent_grads)

Residuals:
   Min     1Q Median     3Q    Max 
-17261  -5474  -1007   3502  57604 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)    56093       1705   32.90   <2e-16 ***
ShareWomen    -30670       2987  -10.27   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9031 on 170 degrees of freedom
  (1 observation deleted due to missingness)
Multiple R-squared:  0.3828,    Adjusted R-squared:  0.3791 
F-statistic: 105.4 on 1 and 170 DF,  p-value: < 2.2e-16

The results tell us that everyone starts their median income at $56,093, this is the constant. Majors with higher proportion of women graduates are predicted $30,670 lower median earnings than others. So if 100% of graduates were women for a major, the predicted income would be $56,093-$30,670= $25,423 where as for men, lets assume, would be $56,093. Now lets say the share of women are .50,being 50%, so they would be earning $15,335(50% of $30,670) lower than others; which in this case would be $40,758 ($56,093-$15,335). Lets see what would happen if we were to add another independent variable, college majors (categories).

Regression Model with two independent variables

Regressionmodel2<- lm(MedianEarnings ~ ShareWomen + CollegeMajorCategory, data = recent_grads)
summary(Regressionmodel2)

Call:
lm(formula = MedianEarnings ~ ShareWomen + CollegeMajorCategory, 
    data = recent_grads)

Residuals:
   Min     1Q Median     3Q    Max 
-19940  -3932   -770   2674  50743 

Coefficients:
                                                        Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                              41529.6     3010.6  13.794  < 2e-16 ***
ShareWomen                                              -15837.7     4199.4  -3.771  0.00023 ***
CollegeMajorCategoryArts                                  1093.4     3714.8   0.294  0.76889    
CollegeMajorCategoryBiology & Life Science                4191.6     3273.5   1.280  0.20230    
CollegeMajorCategoryBusiness                              9661.6     3247.2   2.975  0.00340 ** 
CollegeMajorCategoryCommunications & Journalism           3397.7     4601.5   0.738  0.46140    
CollegeMajorCategoryComputers & Mathematics               6153.6     3371.6   1.825  0.06991 .  
CollegeMajorCategoryEducation                             2675.0     3422.6   0.782  0.43566    
CollegeMajorCategoryEngineering                          19636.6     2927.4   6.708 3.49e-10 ***
CollegeMajorCategoryHealth                                7888.7     3670.6   2.149  0.03318 *  
CollegeMajorCategoryHumanities & Liberal Arts              389.8     3282.2   0.119  0.90561    
CollegeMajorCategoryIndustrial Arts & Consumer Services    348.9     3761.9   0.093  0.92623    
CollegeMajorCategoryInterdisciplinary                     5679.7     8002.0   0.710  0.47891    
CollegeMajorCategoryLaw & Public Policy                   8330.3     4168.6   1.998  0.04743 *  
CollegeMajorCategoryPhysical Sciences                     8416.8     3450.6   2.439  0.01585 *  
CollegeMajorCategoryPsychology & Social Work              1151.8     3873.6   0.297  0.76661    
CollegeMajorCategorySocial Science                        4588.3     3567.2   1.286  0.20027    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 7450 on 155 degrees of freedom
  (1 observation deleted due to missingness)
Multiple R-squared:  0.617, Adjusted R-squared:  0.5775 
F-statistic: 15.61 on 16 and 155 DF,  p-value: < 2.2e-16

The constant median income in this model is $41,529.60 and the negative slope is -$15,837.70. Meaning, for every major with 100% women graduates, they tend to earn $15,837.70 less. As we can see not all colelge major categories are statistically significant in the model. Engineering, Business, Health, physical sciences and law & public policy are of those college majors which show there is significance between the median incomes and proportion of share of women. For Business, we see that 48% were women graduates so what would be the median income for women? It would be $43,588.50 ($15,837.70 X.48 = $7,602.09 -> $41,529.60 - $7,602.09 = $33,927.50 +$9,661 = $43,588.50).The reference major category is argiculture, meaning with 0% of women graduated with this major, the estimate median earning would be $41,529.60.

Interaction

Is the share of women prediciting Median Income differently for different majors

M3<- lm(MedianEarnings ~ ShareWomen*CollegeMajorCategory, data = recent_grads)
summary(M3)

Call:
lm(formula = MedianEarnings ~ ShareWomen * CollegeMajorCategory, 
    data = recent_grads)

Residuals:
   Min     1Q Median     3Q    Max 
-24833  -3461   -320   2413  47156 

Coefficients: (1 not defined because of singularities)
                                                                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                                           40396       5716   7.067 6.71e-11 ***
ShareWomen                                                           -13040      12716  -1.025   0.3069    
CollegeMajorCategoryArts                                              12233      13992   0.874   0.3834    
CollegeMajorCategoryBiology & Life Science                            -4498      23713  -0.190   0.8498    
CollegeMajorCategoryBusiness                                          20981       9687   2.166   0.0320 *  
CollegeMajorCategoryCommunications & Journalism                      -12236      30963  -0.395   0.6933    
CollegeMajorCategoryComputers & Mathematics                            1568       8792   0.178   0.8587    
CollegeMajorCategoryEducation                                         -5508      11054  -0.498   0.6190    
CollegeMajorCategoryEngineering                                       28012       6739   4.157 5.58e-05 ***
CollegeMajorCategoryHealth                                            -5728      16072  -0.356   0.7221    
CollegeMajorCategoryHumanities & Liberal Arts                         -4922      10742  -0.458   0.6475    
CollegeMajorCategoryIndustrial Arts & Consumer Services                1728       7138   0.242   0.8090    
CollegeMajorCategoryInterdisciplinary                                  4657       9101   0.512   0.6097    
CollegeMajorCategoryLaw & Public Policy                               17833      13013   1.370   0.1727    
CollegeMajorCategoryPhysical Sciences                                 -4006      10349  -0.387   0.6993    
CollegeMajorCategoryPsychology & Social Work                          21403      25567   0.837   0.4039    
CollegeMajorCategorySocial Science                                     9840      12099   0.813   0.4174    
ShareWomen:CollegeMajorCategoryArts                                  -19374      24297  -0.797   0.4266    
ShareWomen:CollegeMajorCategoryBiology & Life Science                 13932      41065   0.339   0.7349    
ShareWomen:CollegeMajorCategoryBusiness                              -23876      20137  -1.186   0.2377    
ShareWomen:CollegeMajorCategoryCommunications & Journalism            22670      47606   0.476   0.6347    
ShareWomen:CollegeMajorCategoryComputers & Mathematics                15548      23859   0.652   0.5157    
ShareWomen:CollegeMajorCategoryEducation                               9650      17758   0.543   0.5877    
ShareWomen:CollegeMajorCategoryEngineering                           -33111      18752  -1.766   0.0796 .  
ShareWomen:CollegeMajorCategoryHealth                                 15753      22612   0.697   0.4872    
ShareWomen:CollegeMajorCategoryHumanities & Liberal Arts               7404      18966   0.390   0.6968    
ShareWomen:CollegeMajorCategoryIndustrial Arts & Consumer Services    -3500      15710  -0.223   0.8240    
ShareWomen:CollegeMajorCategoryInterdisciplinary                         NA         NA      NA       NA    
ShareWomen:CollegeMajorCategoryLaw & Public Policy                   -20101      26435  -0.760   0.4483    
ShareWomen:CollegeMajorCategoryPhysical Sciences                      23853      20688   1.153   0.2509    
ShareWomen:CollegeMajorCategoryPsychology & Social Work              -26863      33705  -0.797   0.4268    
ShareWomen:CollegeMajorCategorySocial Science                        -10232      22633  -0.452   0.6519    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 7422 on 141 degrees of freedom
  (1 observation deleted due to missingness)
Multiple R-squared:  0.6542,    Adjusted R-squared:  0.5806 
F-statistic: 8.891 on 30 and 141 DF,  p-value: < 2.2e-16

We include a interaction in a model when we suspect that one independent variable may effect on the other independent varaible. Because we don’t have too much information about this dataset and do not know how each major may or may not effect median earnings compared to major with higher proportion of women graduates. Additionally, we are running a regression to test if the share proportion of women graduates in each major category predicts the median income. It is not possible using this data set to compare the median income between major categories as some majors are women dominant and tend to have lower earnings than higher earning majors. For example, incomes in education tend to be lower than those in engineering and also have higher proportion of women graduates. We can also not conclude that higher proportion of women effect median earnings to lower compared to those major with lesser women graduates as it may be as mentioned above, some majors are women dominant as well as the high percentage of women graduates in one major could be because women go for low income majors so the share women proportion is high for that major. Nevertheless, this model shows that no statistically significance between share proportion of women graduates and colelge major categories.

All 4 - Formatted Tables

screenreg(list(Regressionmodel,Regressionmodel2,M3))

===============================================================================================================
                                                                    Model 1        Model 2        Model 3      
---------------------------------------------------------------------------------------------------------------
(Intercept)                                                          56093.31 ***   41529.60 ***   40395.72 ***
                                                                     (1705.11)      (3010.61)      (5716.43)   
ShareWomen                                                          -30669.94 ***  -15837.66 ***  -13039.80    
                                                                     (2987.01)      (4199.38)     (12715.75)   
CollegeMajorCategoryArts                                                             1093.43       12233.42    
                                                                                    (3714.82)     (13991.66)   
CollegeMajorCategoryBiology & Life Science                                           4191.59       -4498.32    
                                                                                    (3273.51)     (23712.88)   
CollegeMajorCategoryBusiness                                                         9661.59 **    20980.64 *  
                                                                                    (3247.19)      (9686.96)   
CollegeMajorCategoryCommunications & Journalism                                      3397.66      -12236.41    
                                                                                    (4601.52)     (30963.44)   
CollegeMajorCategoryComputers & Mathematics                                          6153.60        1567.61    
                                                                                    (3371.59)      (8792.06)   
CollegeMajorCategoryEducation                                                        2675.01       -5508.37    
                                                                                    (3422.60)     (11054.35)   
CollegeMajorCategoryEngineering                                                     19636.60 ***   28012.04 ***
                                                                                    (2927.39)      (6739.31)   
CollegeMajorCategoryHealth                                                           7888.75 *     -5728.20    
                                                                                    (3670.65)     (16072.47)   
CollegeMajorCategoryHumanities & Liberal Arts                                         389.82       -4921.85    
                                                                                    (3282.19)     (10741.78)   
CollegeMajorCategoryIndustrial Arts & Consumer Services                               348.89        1728.07    
                                                                                    (3761.88)      (7137.58)   
CollegeMajorCategoryInterdisciplinary                                                5679.67        4656.68    
                                                                                    (8001.99)      (9101.06)   
CollegeMajorCategoryLaw & Public Policy                                              8330.27 *     17832.80    
                                                                                    (4168.59)     (13012.81)   
CollegeMajorCategoryPhysical Sciences                                                8416.76 *     -4006.24    
                                                                                    (3450.61)     (10348.92)   
CollegeMajorCategoryPsychology & Social Work                                         1151.79       21402.78    
                                                                                    (3873.65)     (25567.35)   
CollegeMajorCategorySocial Science                                                   4588.32        9840.28    
                                                                                    (3567.18)     (12098.56)   
ShareWomen:CollegeMajorCategoryArts                                                               -19373.65    
                                                                                                  (24296.98)   
ShareWomen:CollegeMajorCategoryBiology & Life Science                                              13932.24    
                                                                                                  (41064.92)   
ShareWomen:CollegeMajorCategoryBusiness                                                           -23876.54    
                                                                                                  (20136.71)   
ShareWomen:CollegeMajorCategoryCommunications & Journalism                                         22670.49    
                                                                                                  (47605.67)   
ShareWomen:CollegeMajorCategoryComputers & Mathematics                                             15548.46    
                                                                                                  (23858.71)   
ShareWomen:CollegeMajorCategoryEducation                                                            9649.93    
                                                                                                  (17757.49)   
ShareWomen:CollegeMajorCategoryEngineering                                                        -33111.41    
                                                                                                  (18752.52)   
ShareWomen:CollegeMajorCategoryHealth                                                              15753.09    
                                                                                                  (22612.26)   
ShareWomen:CollegeMajorCategoryHumanities & Liberal Arts                                            7404.17    
                                                                                                  (18965.62)   
ShareWomen:CollegeMajorCategoryIndustrial Arts & Consumer Services                                 -3499.69    
                                                                                                  (15709.79)   
ShareWomen:CollegeMajorCategoryLaw & Public Policy                                                -20101.01    
                                                                                                  (26434.71)   
ShareWomen:CollegeMajorCategoryPhysical Sciences                                                   23853.05    
                                                                                                  (20688.47)   
ShareWomen:CollegeMajorCategoryPsychology & Social Work                                           -26862.79    
                                                                                                  (33705.44)   
ShareWomen:CollegeMajorCategorySocial Science                                                     -10231.73    
                                                                                                  (22632.83)   
---------------------------------------------------------------------------------------------------------------
R^2                                                                      0.38           0.62           0.65    
Adj. R^2                                                                 0.38           0.58           0.58    
Num. obs.                                                              172            172            172       
RMSE                                                                  9030.92        7450.29        7422.39    
===============================================================================================================
*** p < 0.001, ** p < 0.01, * p < 0.05

In conclusion, we see the best model for this regression would be model 3 in context to R^2 but as we know there is not statistically significance we will say Model 2 is the best model to test if higher proportion of women graduates within a major predicts the median income to be lower or higher. Also, we can see the adjusted R^2 is same for Model 2 & Model 3.This may be because it has more independent variables than Model 1. In some cases, the more independent variables that are considered in a model, the more stronger the model is and gives apt outputs. This regression could not be fully tested due to the small number of observations as well as not having full detail on the data set.