library(ggplot2)


ggplot(salesData, aes(x = expenditures, y = sales)) +
  geom_point() +
  labs(title = "Scatter Plot of Sales vs Advertisement Expenditure",
       x = "Advertisement Expenditure ($1000)",
       y = "Sales ($1000)") +
  theme_minimal()


correlation <- cor(salesData$expenditures, salesData$sales)
print(paste("Correlation Coefficient:", correlation))

cor_test <- cor.test(salesData$expenditures, salesData$sales)
print(cor_test)


lm_model <- lm(sales ~ expenditures, data = salesData)
coefficients <- summary(lm_model)$coefficients
print(coefficients)

ggplot(salesData, aes(x = expenditures, y = sales)) +
  geom_point() +
  geom_smooth(method = "lm", se = FALSE, color = "blue") +
  labs(title = "Scatter Plot of Sales vs Advertisement Expenditure with Regression Line",
       x = "Advertisement Expenditure ($1000)",
       y = "Sales ($1000)") +
  theme_minimal()


r_squared <- summary(lm_model)$r.squared
print(paste("R²:", r_squared))


se <- summary(lm_model)$sigma
print(paste("Standard Error of the Estimate (se):", se))


sb1 <- summary(lm_model)$coefficients[2, "Std. Error"]
print(paste("Standard Error of the Slope (sb1):", sb1))



slope_test <- summary(lm_model)$coefficients[2, ]
print(slope_test)



new_expenditure <- data.frame(expenditures = 3260)
predicted_sales <- predict(lm_model, new_expenditure)
print(paste("Predicted Sales for $3260 Expenditure:", predicted_sales))



prediction_interval <- predict(lm_model, new_expenditure, interval = "prediction", level = 0.95)
print(prediction_interval)