# Polynomial Regression

rm(list = ls())

# Importing the dataset
dataset <- read.csv(file.path(getwd(),'Data/Position_Salaries.csv'))
dataset <- dataset[2:3]

plot(x = dataset$Level, y = dataset$Salary) # ploting data on the fly ;)

# no need to split data because the dataset is small
# no need for feature scaling with regression

# Fitting Linear Regression to the dataset
# instead of using "." we can just use the name of the column since it is only one column
lin_reg <- lm(formula = Salary ~ .,
             data = dataset)


# Fitting Polynomial Regression to the dataset
dataset$Level2 <- dataset$Level^2
dataset$Level3 <- dataset$Level^3
dataset$Level4 <- dataset$Level^4
poly_reg <- lm(formula = Salary ~ ., data = dataset)

# However, i found an easier way to do polynomial regression
# the keyword "poly" help us decide the level of polynomial
# in the previous code we are doing it manually , stupid!
poly_reg <- lm(formula = Salary ~ poly (Level, 4), data = dataset)


# the above code is using orthogonal poly regression
# however, if we dont want that, we can use:
poly_reg <- lm(formula = Salary ~ poly (Level, 4, raw = TRUE), data = dataset)

# I added this part
# Plot of fitted vs residuals.
# No clear pattern should show in the residual plot if the model is a good fit

# for the simple linear regression
plot(fitted(lin_reg), residuals(lin_reg))

# for the polynomial linear regression
plot(fitted(poly_reg), residuals(poly_reg))

# Visualising the Linear Regression results
if (!require("ggplot2"))
  install.packages("ggplot2") # to install the package if you don't have it
ggplot() +
  geom_point(aes(x = dataset$Level, y = dataset$Salary),
             colour = 'red') +
  geom_line(aes(x = dataset$Level, y = predict(lin_reg, newdata = dataset)),
            colour = 'blue') +
  ggtitle('Truth or Bluff (Linear Regression)') +
  xlab('Level') +
  ylab('Salary')

# Visualising the Polynomial Regression results
# install.packages('ggplot2')
library(ggplot2)
ggplot() +
  geom_point(aes(x = dataset$Level, y = dataset$Salary),
             colour = 'red') +
  geom_line(aes(x = dataset$Level, y = predict(poly_reg, newdata = dataset)),
            colour = 'blue') +
  ggtitle('Truth or Bluff (Polynomial Regression)') +
  xlab('Level') +
  ylab('Salary') +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

# Visualising the Regression Model results (for higher resolution and smoother curve)
# install.packages('ggplot2')
library(ggplot2)
x_grid = seq(min(dataset$Level), max(dataset$Level), 0.1)
ggplot() +
  geom_point(aes(x = dataset$Level, y = dataset$Salary),
             colour = 'red') +
  geom_line(aes(x = x_grid, y = predict(poly_reg,
                                        newdata = data.frame(Level = x_grid,
                                                             Level2 = x_grid^2,
                                                             Level3 = x_grid^3,
                                                             Level4 = x_grid^4))),
            colour = 'blue') +
  ggtitle('Truth or Bluff (Polynomial Regression)') +
  xlab('Level') +
  ylab('Salary') +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5))

# Predicting a new result with Linear Regression
predict(lin_reg, data.frame(Level = 6.5))

# Predicting a new result with Polynomial Regression
predict(poly_reg, data.frame(Level = 6.5,
                             Level2 = 6.5^2,
                             Level3 = 6.5^3,
                             Level4 = 6.5^4))