Polynomial Regression

Importing the dataset

dataset = read.csv('C:/RClass/Position_Salaries.csv')
dataset = dataset[2:3]

Splitting the dataset into the Training set and Test set

# install.packages('caTools')
# library(caTools)
# set.seed(2023)
# split = sample.split(dataset$Salary, SplitRatio = 0.8)
# training_set = subset(dataset, split == TRUE)
# test_set = subset(dataset, split == FALSE)

Feature Scaling

# training_set = scale(training_set)
# test_set = scale(test_set)

Fitting Linear Regression to the dataset

lin_reg = lm(formula = Salary ~., 
             data = dataset)
summary(lin_reg)

## 
## Call:
## lm(formula = Salary ~ ., data = dataset)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -170818 -129720  -40379   65856  386545 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  -195333     124790  -1.565  0.15615   
## Level          80879      20112   4.021  0.00383 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 182700 on 8 degrees of freedom
## Multiple R-squared:  0.669,  Adjusted R-squared:  0.6277 
## F-statistic: 16.17 on 1 and 8 DF,  p-value: 0.003833

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)
summary(poly_reg)

## 
## Call:
## lm(formula = Salary ~ ., data = dataset)
## 
## Residuals:
##      1      2      3      4      5      6      7      8      9     10 
##  -8357  18240   1358 -14633 -11725   6725  15997  10006 -28695  11084 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  184166.7    67768.0   2.718  0.04189 * 
## Level       -211002.3    76382.2  -2.762  0.03972 * 
## Level2        94765.4    26454.2   3.582  0.01584 * 
## Level3       -15463.3     3535.0  -4.374  0.00719 **
## Level4          890.2      159.8   5.570  0.00257 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 20510 on 5 degrees of freedom
## Multiple R-squared:  0.9974, Adjusted R-squared:  0.9953 
## F-statistic: 478.1 on 4 and 5 DF,  p-value: 1.213e-06

Visualizing the Linear Regression results

# install.packages('ggplot2')
library(ggplot2)

## Warning: package 'ggplot2' was built under R version 4.1.3

ggplot() + 
  geom_point(aes(x=dataset$Level, y=dataset$Salary), color='red') +
  geom_line(aes(x=dataset$Level, y=predict(lin_reg, newdata=dataset)), color='blue') +
  ggtitle('Truth or Bluff (Linear Regression)') +
  xlab('Level') + ylab('Salary')

Visualizing the Polynomial Regression results

ggplot() + 
  geom_point(aes(x=dataset$Level, y=dataset$Salary), color='red') +
  geom_line(aes(x=dataset$Level, y=predict(poly_reg, newdata=dataset)), color='blue') +
  ggtitle('Truth or Bluff (Polynomial Regression)') +
  xlab('Level') + ylab('Salary')

Predicting a new result with Linear Regression

y_pred = predict(lin_reg, data.frame(Level=6.5))
y_pred

##        1 
## 330378.8

Predicting a new result with Polynomial Regression

y_pred = predict(poly_reg, data.frame(Level=6.5, 
                                      Level2=6.5^2, 
                                      Level3=6.5^3, 
                                      Level4=6.5^4))
y_pred

##        1 
## 158862.5

Visualising the Regression Model results (for higher resolution and smoother curve)

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')