Assignment 1

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Pasadena City College *

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Course

140

Subject

Economics

Date

Feb 20, 2024

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Pages

7

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Assignment 1 2024-01-21 2.28(a) Summary: library (POE5Rdata) summary ( lm (wage ~ educ, cps5_small)) ## ## Call: ## lm(formula = wage ~ educ, data = cps5_small) ## ## Residuals: ## Min 1Q Median 3Q Max ## -31.785 -8.381 -3.166 5.708 193.152 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) -10.4000 1.9624 -5.3 1.38e-07 *** ## educ 2.3968 0.1354 17.7 < 2e-16 *** ## --- ## Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 ## ## Residual standard error: 13.55 on 1198 degrees of freedom ## Multiple R-squared: 0.2073, Adjusted R-squared: 0.2067 ## F-statistic: 313.3 on 1 and 1198 DF, p-value: < 2.2e-16 1
par ( mfrow = c ( 1 , 2 )) hist (cps5_small $ wage, xlab= "Earnings Per Hour" , main= "Histogram of Wages" ) hist (cps5_small $ educ, xlab= "Years of Education" , main= "Historgram of Education" ) Histogram of Wages Earnings Per Hour Frequency 0 50 100 200 0 100 300 500 Historgram of Education Years of Education Frequency 0 5 10 15 20 0 50 100 200 300 The histogram for WAGE is right-skewed, indicating that most of the observations lie between the hourly earnings of 0 to 50. The median shows that half of the sample earns more than 19.3 dollars per hour, while the mean is at 23.64 dollars an hour. The maximum earned in this sample is 221.1 dollars per hour and the least earned in this sample is 3.94 dollars per hour. The histogram for EDUC , on the other hand, is left-skewed, indicating that most people had at least 12 years of education. There are a few observations at less than 12, representing those who did not complete high school. The median shows that half of the sample has had more than 14 years of education, while the mean is at 14.2 years. This means that half of the sample only reached two years of a bachelor’s degree or have finished an associate’s. 2.28(b) regout <- lm (wage ~ educ, cps5_small) coef (regout) ## (Intercept) educ ## -10.399959 2.396761 Estimated Equation: WAGE = -10.399959 + 2.396761 EDUC The slope of 2.396761 represents the estimated increase in the expected hourly wage rate for an extra year of education. The intercept -10.399959 represents the estimated wage rate of a worker with no years of education. It should not be considered meaningful as it is not possible to have a negative hourly wage rate. 2
2.28(c) plot (cps5_small $ educ,regout $ residuals, xlab= "EDUC" , ylab= "RESIDUAL" , main= "Residual against Education" ) 0 5 10 15 20 0 50 100 150 200 Residual against Education EDUC RESIDUAL There is a pattern evident; as EDUC increases, the magnitude of the residuals also increases, suggesting that the error variance is larger for larger values of EDUC – a violation of the assumptions. If the assumptions SR1-SR5 hold, there should not be any patterns evident in the residuals. 2.28(d) coef ( lm (wage ~ educ, cps5_small, subset = (female == 0 ))) ## (Intercept) educ ## -8.284936 2.378471 coef ( lm (wage ~ educ, cps5_small, subset = (female == 1 ))) ## (Intercept) educ ## -16.602785 2.659487 coef ( lm (wage ~ educ, cps5_small, subset = (black == 0 ))) ## (Intercept) educ ## -10.474710 2.417769 coef ( lm (wage ~ educ, cps5_small, subset = (black == 1 ))) ## (Intercept) educ ## -6.254114 1.923330 Male: WAGE = -8.284936 + 2.378471 EDUC 3
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Female: WAGE = -16.602785 + 2.659487 EDUC White: WAGE = -10.474710 + 2.417769 EDUC Black: WAGE = -6.254114 + 1.923330 EDUC The variables male, female, black, and white are all indicator variables, meaning they either are or are not that specific demographic. With a slope of 1.92330, in comparison to all other variables, the estimated increase in the expected hourly wage rate for an extra year of education for black workers is relatively smaller. On the other hand, with every extra year of education, female workers had the highest estimated increase in the expected hourly wage rate. 4