Homework 3
2025-05-19
1. Sample description
The dataset includes 200 public service employees, with information on their annual salary (€), years of employment, and gender. Of the sample, 131 are male and 69 are female. Salaries range from approximately €22,000 to €296,000, with an average of around €122,000. Years of employment range from under 2 years to over 40, with an average of about 20 years. This dataset provides a strong basis to explore how salary relates to experience and whether gender plays a role.
SalaryData = read.xlsx("SalaryData.xlsx")
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## Female Male
## 69 131summary(SalaryData$salary)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 30028 60076 93164 108491 150437 255381sd(SalaryData$salary)## [1] 60116.36summary(SalaryData$years_exp)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.007167 7.749079 16.662402 15.666479 22.823554 29.666752sd(SalaryData$years_exp)## [1] 8.760716
2. Association between years and salary as scatterplot.
The scatterplot below shows a positive association between years of employment and salary. However, the relationship appears to be nonlinear—salaries rise with experience, but not at a constant rate. There may be diminishing returns at higher experience levels.
plot(SalaryData$years_exp, SalaryData$salary,
main = "Scatterplot: Years of Experience vs. Salary",
xlab = "Years of Experience", ylab = "Salary (€)",
pch = 19, col = "steelblue")
3. Estimate salary by years of employment
To better estimate the relationship, we log-transformed the salary variable to linearize the association. A linear model was then fitted with log(salary) as the dependent variable and years of experience as the predictor.
SalaryData$log_salary = log(SalaryData$salary)
model = lm(log_salary ~ years_exp, data = SalaryData)
summary(model)##
## Call:
## lm(formula = log_salary ~ years_exp, data = SalaryData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.74993 -0.11686 0.00666 0.11146 0.77461
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.436444 0.032197 324.14 <2e-16 ***
## years_exp 0.063322 0.001795 35.28 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2218 on 198 degrees of freedom
## Multiple R-squared: 0.8628, Adjusted R-squared: 0.8621
## F-statistic: 1245 on 1 and 198 DF, p-value: < 2.2e-16
4. Interpretation
The regression model shows a strong relationship between log-transformed salary and years of experience, with an R-squared of around 0.86. The slope of the model is approximately 0.063, which means that for each additional year of experience, salary increases by about 6.3% on average. This supports the idea that salary grows exponentially with experience rather than linearly.
5. (Voluntary) Gender effects
To explore gender effects, we fit separate models for male and female employees.
model_male = lm(log_salary ~ years_exp, data = subset(SalaryData, gender == "Male"))
model_female = lm(log_salary ~ years_exp, data = subset(SalaryData, gender == "Female"))
summary(model_male)##
## Call:
## lm(formula = log_salary ~ years_exp, data = subset(SalaryData,
## gender == "Male"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.29310 -0.10494 -0.03192 0.07773 0.66850
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.54381 0.02735 385.48 <2e-16 ***
## years_exp 0.06296 0.00165 38.17 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1685 on 129 degrees of freedom
## Multiple R-squared: 0.9186, Adjusted R-squared: 0.918
## F-statistic: 1457 on 1 and 129 DF, p-value: < 2.2e-16summary(model_female)##
## Call:
## lm(formula = log_salary ~ years_exp, data = subset(SalaryData,
## gender == "Female"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.39797 -0.04687 -0.00449 0.08348 0.16695
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.891181 0.036259 272.79 <2e-16 ***
## years_exp 0.081904 0.001789 45.79 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1095 on 67 degrees of freedom
## Multiple R-squared: 0.969, Adjusted R-squared: 0.9686
## F-statistic: 2096 on 1 and 67 DF, p-value: < 2.2e-16While both models show a positive relationship between experience and salary, the slopes and intercepts differ slightly. This could indicate gender-based differences in salary progression, which would require further investigation to confirm and explain.