R Notebook

# Import data set
dataset <-  read.csv("G:\\RStudio\\udemy\\ml\\Machine Learning AZ\\Part 2 - Regression\\Section 6 - Polynomial Regression\\Polynomial_Regression\\Position_Salaries.csv")
head(dataset, n = 10)

# Polynomial Regression
# taking care of missing values
# Test for missing values
sum(is.na(dataset$Position))

[1] 0

sum(is.na(dataset$Level))

[1] 0

sum(is.na(dataset$Salary))

[1] 0

There is no missing values in the dataset.

# We want to use only columns 2 and 3
dataset <-  dataset[2:3]
head(dataset)

The while the next step should be to split the dataset, since this dataset is small, we will use the full dataset.

# feature scaling
# in this case for polynomial, no need for feature scaling. 

# build the linear model for comparison with polynomial regression
lreg <-  lm(formula = Salary ~ Level, data = dataset)
summary(lreg)

Call:
lm(formula = Salary ~ Level, 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

# building the polynomial regression model
# add a new column in the dataframe
dataset$Level2 <-  dataset$Level^2
dataset$Level3 <-  dataset$Level^3
preg <-  lm(formula = Salary ~ .,
            data = dataset)
summary(preg)

Call:
lm(formula = Salary ~ ., data = dataset)

Residuals:
   Min     1Q Median     3Q    Max 
-75695 -28148   7091  29256  49538 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)   
(Intercept) -121333.3    97544.8  -1.244  0.25994   
Level        180664.3    73114.5   2.471  0.04839 * 
Level2       -48549.0    15081.0  -3.219  0.01816 * 
Level3         4120.0      904.3   4.556  0.00387 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 50260 on 6 degrees of freedom
Multiple R-squared:  0.9812,    Adjusted R-squared:  0.9718 
F-statistic: 104.4 on 3 and 6 DF,  p-value: 1.441e-05

# Visualising the Linear Regression results
# make sure you have installed the ggplot package
library(ggplot2)
ggplot() +
  geom_point(aes(x = dataset$Level, y = dataset$Salary), colour="red") +
  geom_line(aes(x = dataset$Level, y = predict(lreg, newdata = dataset)), colour="blue")+
  ggtitle("Truth or Bluff")+
  xlab("Levels") +
  ylab("Salary")

# visualizing polynomial regression
ggplot() +
  geom_point(aes(x = dataset$Level, y = dataset$Salary), colour = "red") +
  geom_line(aes(x = dataset$Level, y = predict(preg, newdata = dataset)), colour = "blue")+
  ggtitle("Truth or Bluff (Polynomial-level3)") +
  xlab("Levels") +
  ylab("Salary")

# giving it more fit. by adding more levels 
dataset$Level4 <-  dataset$Level^4
head(dataset)

# recompute preg
preg <-  lm(formula = Salary ~ .,
            data = dataset)
summary(preg)

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

ggplot() +
  geom_point(aes(x = dataset$Level, y = dataset$Salary), colour = "red") +
  geom_line(aes(x = dataset$Level, y = predict(preg, newdata = dataset)), colour = "blue")+
  ggtitle("Truth or Bluff (Polynomial-level4)") +
  xlab("Levels") +
  ylab("Salary")

# Predicting a new result with Linear Regression
# make a prediction for a single level 
# so syntax is going to change
y_pred <-  predict(lreg, data.frame(Level = 6.5))
y_pred

       1 
330378.8 

# predicting a result with polynomial Regression
y_pred <-  predict(preg, data.frame(Level = 6.5, Level2 = 6.5^2, Level3 = 6.5^3, Level4= 6.5^4))
y_pred

       1 
158862.5 

So the 160K that the person was asking for is not far from what we predicted.