1. Sample description

The dataset contains salary information, years of employment, and gender of the public service employees.

# replace this by a basic sample description (by applying 
# Clean column names to avoid issues with spaces
names(df) <- trimws(names(df))

# Convert data types 
df$salary <- as.numeric(df$salary)
df$years <- as.numeric(df$years)
df$gender <- as.factor(df$gender)

# Number of rows (observations)
nrow(df)
## [1] 200
# Frequency table for gender
table(df$gender)
## 
## Female   Male 
##     69    131
# Means
mean_salary <- mean(df$salary)
mean_years <- mean(df$years)

# Standard deviations
sd_salary <- sd(df$salary)
sd_years <- sd(df$years)
summary(df$salary)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   30028   60076   93164  108491  150437  255381


2. Association between years and salary as scatterplot.

The scatterplot displays the correlation between years of employment and salary. A positive relationship is evident—salaries tend to rise with more years on the job. However, the trend may not be strictly linear, as salary increases appear to level off with greater experience.

# Scatterplot of Years (independent) vs Salary (dependent)
plot(x=df$years, y=df$salary)
abline(lm(salary ~ years, data = df), col = "blue", lwd = 2)

# replace this by plot(independent variable, dependent variable)


3. Estimate salary by years of employment

A non-linear relationship is observed between salary and years of employment. To make this relationship more linear, we apply a logarithmic transformation to the salary variable and then fit a linear regression model.

df$log_salary <- log(df$salary)

model <- lm(log_salary ~ years, data = df)
summary(model)
## 
## Call:
## lm(formula = log_salary ~ years, data = df)
## 
## 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        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 model indicates that salary tends to rise with additional years of education. Specifically, each extra year of education is associated with an increase in salary of approximately 0.0633. This relationship is statistically significant, highlighting education as a key predictor of salary.


0# replace this by two regression models, separated by gender. 
## [1] 0

SOME TEXT HERE TO INTERPRET YOUR MODEL OUTPUT.