library(dplyr)
library(wooldridge)
data("wage2")model1 <- lm(log(wage) ~ educ + exper + tenure + married + black + south + urban, data = wage2)
summary(model1)##
## Call:
## lm(formula = log(wage) ~ educ + exper + tenure + married + black +
## south + urban, data = wage2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.98069 -0.21996 0.00707 0.24288 1.22822
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.395497 0.113225 47.653 < 2e-16 ***
## educ 0.065431 0.006250 10.468 < 2e-16 ***
## exper 0.014043 0.003185 4.409 1.16e-05 ***
## tenure 0.011747 0.002453 4.789 1.95e-06 ***
## married 0.199417 0.039050 5.107 3.98e-07 ***
## black -0.188350 0.037667 -5.000 6.84e-07 ***
## south -0.090904 0.026249 -3.463 0.000558 ***
## urban 0.183912 0.026958 6.822 1.62e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3655 on 927 degrees of freedom
## Multiple R-squared: 0.2526, Adjusted R-squared: 0.2469
## F-statistic: 44.75 on 7 and 927 DF, p-value: < 2.2e-16Holding other factors fixed, the approximate difference in monthly salary between blacks and nonblacks is -18.85%. In other words, black people approximately received 18.85% less in salary in comparison with nonblack people, holding other factors fixed. The p-value indicate that this is a statistically significant difference.
model2 <- lm(log(wage) ~ educ + exper + tenure + married + black + south + urban + I(exper^2) + I(tenure^2), data = wage2)
summary(model2)##
## Call:
## lm(formula = log(wage) ~ educ + exper + tenure + married + black +
## south + urban + I(exper^2) + I(tenure^2), data = wage2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.98236 -0.21972 -0.00036 0.24078 1.25127
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.3586756 0.1259143 42.558 < 2e-16 ***
## educ 0.0642761 0.0063115 10.184 < 2e-16 ***
## exper 0.0172146 0.0126138 1.365 0.172665
## tenure 0.0249291 0.0081297 3.066 0.002229 **
## married 0.1985470 0.0391103 5.077 4.65e-07 ***
## black -0.1906636 0.0377011 -5.057 5.13e-07 ***
## south -0.0912153 0.0262356 -3.477 0.000531 ***
## urban 0.1854241 0.0269585 6.878 1.12e-11 ***
## I(exper^2) -0.0001138 0.0005319 -0.214 0.830622
## I(tenure^2) -0.0007964 0.0004710 -1.691 0.091188 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3653 on 925 degrees of freedom
## Multiple R-squared: 0.255, Adjusted R-squared: 0.2477
## F-statistic: 35.17 on 9 and 925 DF, p-value: < 2.2e-16anova(model2, lm(log(wage) ~ educ + exper + tenure + married + black + south + urban, data = wage2))## Analysis of Variance Table
##
## Model 1: log(wage) ~ educ + exper + tenure + married + black + south +
## urban + I(exper^2) + I(tenure^2)
## Model 2: log(wage) ~ educ + exper + tenure + married + black + south +
## urban
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 925 123.42
## 2 927 123.82 -2 -0.39756 1.4898 0.226model3 <- lm(log(wage) ~ educ + exper + tenure + married + black + south + urban + educ*black, data = wage2)
summary(model3)##
## Call:
## lm(formula = log(wage) ~ educ + exper + tenure + married + black +
## south + urban + educ * black, data = wage2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.97782 -0.21832 0.00475 0.24136 1.23226
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.374817 0.114703 46.859 < 2e-16 ***
## educ 0.067115 0.006428 10.442 < 2e-16 ***
## exper 0.013826 0.003191 4.333 1.63e-05 ***
## tenure 0.011787 0.002453 4.805 1.80e-06 ***
## married 0.198908 0.039047 5.094 4.25e-07 ***
## black 0.094809 0.255399 0.371 0.710561
## south -0.089450 0.026277 -3.404 0.000692 ***
## urban 0.183852 0.026955 6.821 1.63e-11 ***
## educ:black -0.022624 0.020183 -1.121 0.262603
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3654 on 926 degrees of freedom
## Multiple R-squared: 0.2536, Adjusted R-squared: 0.2471
## F-statistic: 39.32 on 8 and 926 DF, p-value: < 2.2e-16anova(model3, lm(log(wage) ~ educ + exper + tenure + married + black + south + urban, data = wage2))## Analysis of Variance Table
##
## Model 1: log(wage) ~ educ + exper + tenure + married + black + south +
## urban + educ * black
## Model 2: log(wage) ~ educ + exper + tenure + married + black + south +
## urban
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 926 123.65
## 2 927 123.82 -1 -0.16778 1.2565 0.2626The return to education does not significantly depend on race in this data.
model4 <- lm(log(wage) ~ educ + exper + tenure + married + black + south + urban + married:black, data = wage2)
summary(model4)##
## Call:
## lm(formula = log(wage) ~ educ + exper + tenure + married + black +
## south + urban + married:black, data = wage2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.98013 -0.21780 0.01057 0.24219 1.22889
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.403793 0.114122 47.351 < 2e-16 ***
## educ 0.065475 0.006253 10.471 < 2e-16 ***
## exper 0.014146 0.003191 4.433 1.04e-05 ***
## tenure 0.011663 0.002458 4.745 2.41e-06 ***
## married 0.188915 0.042878 4.406 1.18e-05 ***
## black -0.240820 0.096023 -2.508 0.012314 *
## south -0.091989 0.026321 -3.495 0.000497 ***
## urban 0.184350 0.026978 6.833 1.50e-11 ***
## married:black 0.061354 0.103275 0.594 0.552602
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3656 on 926 degrees of freedom
## Multiple R-squared: 0.2528, Adjusted R-squared: 0.2464
## F-statistic: 39.17 on 8 and 926 DF, p-value: < 2.2e-16Holding other factors constant, the estimated wage differential between married blacks and married nonblacks is 6.14%. However, since the p-value is 0.5526, this difference is not statistically significant, meaning there is no strong evidence to suggest that the wage differential between married blacks and married nonblacks is different from zero in this sample.