Code Salary and Experience.Rmd

---
title: "Salary and Years of Experience"
output:
  html_document:
    df_print: paged
---

Read in data

```{r}
salary = read.table("salary.csv", header = TRUE, sep = ",")
```

Create scatterplot of years of employment vs. salary and residual plot

```{r}
library(ggplot2)

# Create a scatterplot
ggplot(salary, aes(x = years, y = salary)) +
  geom_point(shape = 21, color = "black", fill = "steelblue", size = 4, stroke = 0.5, alpha = 0.8) +  # Points with outline
  labs(title = "Pre Transformation Salary vs. Experience",
       x = "Years of Employment",
       y = "Salary") +
  ylim(0, 300000) +  # Set y-axis limits
  theme_minimal() +
  theme(plot.title = element_text(hjust = 0.5, size = 16, face = "bold"),
        axis.title = element_text(size = 14),
        axis.text = element_text(size = 12))


# Fit model using untransformed salary
model = lm(salary ~ years, data = salary)

# Residual plot
salary$pred <- predict(model)  # Make predictions
salary$residuals <- rstudent(model)  # Calculate jackknife residuals

# Create the residual plot
ggplot(salary, aes(x = pred, y = residuals)) +
  geom_point(shape = 21, color = "black", fill = "steelblue", size = 4, stroke = 0.5, alpha = 0.8) +  # Points with outline
  geom_hline(yintercept = 0, color = "lightgray", size = 1) +  # Light gray horizontal line
  geom_hline(yintercept = 0, color = "black", size = 0.5) +  # Black outline for the line
  labs(title = "Pre Transformation Residual Plot",
       x = "Predicted Salary",
       y = "Jackknife Residual") +
  theme_minimal() +
  theme(plot.title = element_text(hjust = 0.5, size = 16, face = "bold"),
        axis.title = element_text(size = 14),
        axis.text = element_text(size = 12))
```

Transform response variable using natural log transformation and save in data frame

```{r}
salary$log_salary = log(salary$salary)
```

Create scatterplot and residual plot for years of employment vs. natural log of salary

```{r}
# Scatterplot
ggplot(salary, aes(x = years, y = log_salary)) +
  geom_point(shape = 21, color = "black", fill = "steelblue", size = 4, stroke = 0.5, alpha = 0.8) +  # Points with outline
  labs(title = "Post Transformation log(Salary) vs. Years of Employment",
       x = "Years of Employment",
       y = "Natural Log of Salary") +
  theme_minimal() +
  theme(plot.title = element_text(hjust = 0.5, size = 16, face = "bold"),
        axis.title = element_text(size = 14),
        axis.text = element_text(size = 12))

# Fit model on transformed response
tr_model = lm(log(salary) ~ years, data = salary)

# Residual plot
salary$tr_pred = predict(tr_model)  # Make predictions using transformed model
salary$tr_residuals = rstudent(tr_model)  # Calculate jackknife residuals for transformed model

ggplot(salary, aes(x = tr_pred, y = tr_residuals)) +
  geom_point(shape = 21, color = "black", fill = "steelblue", size = 4, stroke = 0.5, alpha = 0.8) +  # Points with outline
  geom_hline(yintercept = 0, color = "lightgray", size = 1) +  # Light gray horizontal line
  geom_hline(yintercept = 0, color = "black", size = 0.5) +  # Black outline for the line
  labs(title = "Post Transformation Residual Plot",
       x = "Predicted Natural Log of Salary",
       y = "Jackknife Residual") +
  theme_minimal() +
  theme(plot.title = element_text(hjust = 0.5, size = 16, face = "bold"),
        axis.title = element_text(size = 14),
        axis.text = element_text(size = 12))
```

```{r}
summary(tr_model)
summary(model)
```