Revise Linear Regression.ipynb

Kernel: Python 3

Linear regression is a statistical approach for modelling relationship between a dependent variable with a given set of independent variables

# IPython magic to plot interactively on the notebook
%matplotlib notebook

from scipy import linspace, polyval, polyfit, sqrt, stats, randn
from matplotlib.pyplot import plot, title, show, legend

# Linear regression example
# This is a very simple example of using two scipy tools 
# for linear regression, polyfit and stats.linregress

# Sample data creation

# number of points 
n = 50
t = linspace(-5,5,n)
# parameters
a = 0.8
b = -4
x = polyval([a, b], t)
# add some noise
xn = x + randn(n)

# Linear regressison -polyfit - polyfit can be used other orders polys
(ar, br) = polyfit(t, xn, 1)
xr = polyval([ar, br], t)
# compute the mean square error
err = sqrt(sum((xr - xn)**2)/n)
print('Linear regression using polyfit')
print('parameters: a=%.2f b=%.2f \nregression: a=%.2f b=%.2f, ms error= %.3f' % (a, b, ar, br, err))
print('\n')


# Linear regression using stats.linregress
(a_s, b_s, r, tt, stderr) = stats.linregress(t, xn)
print('Linear regression using stats.linregress')
print('parameters: a=%.2f b=%.2f \nregression: a=%.2f b=%.2f, std error= %.3f' % (a,b,a_s,b_s,stderr))
print('\n')

# matplotlib ploting
title('Linear Regression Example')
plot(t, x,'g.--')
plot(t, xn, 'k.')
plot(t, xr, 'r.-')
legend(['original','plus noise', 'regression'])
show();

Linear regression using polyfit
parameters: a=0.80 b=-4.00 
regression: a=0.81 b=-3.76, ms error= 0.965


Linear regression using stats.linregress
parameters: a=0.80 b=-4.00 
regression: a=0.81 b=-3.76, std error= 0.047

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# Importing the libraries
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd

# Importing the dataset
sal = pd.read_excel('Salary.xlsx')
X = sal.iloc[:, :-1].values # create matrix of features
y = sal.iloc[:, 1].values # create dependent variable vector

# Splitting the dataset into the Training set and Test set
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 1/3, random_state = 0) # Change test size

 ## Feature Scaling not needed because the library used to build simple linear regressionc model will take care of that
"""from sklearn.preprocessing import StandardScaler
sc_X = StandardScaler()
X_train = sc_X.fit_transform(X_train)
X_test = sc_X.transform(X_test)
sc_y = StandardScaler()
y_train = sc_y.fit_transform(y_train)"""

'from sklearn.preprocessing import StandardScaler\nsc_X = StandardScaler()\nX_train = sc_X.fit_transform(X_train)\nX_test = sc_X.transform(X_test)\nsc_y = StandardScaler()\ny_train = sc_y.fit_transform(y_train)'

 ## Fitting Simple Linear Regression to the Training Set
from sklearn.linear_model import LinearRegression
## Create object of Linear Regression class by calling it
reg = LinearRegression()

## Fit regressor object to training set by usinig the .fit method of the LinearRegression class
# Fitting Simple Linear Regression to the Training set
# We created a machine (simple linear regression model) and made it learn correlations on the training set so that the machine can predict salary based on its learning experience.
model = reg.fit(X_train,y_train)

## Predicting the Test set results
y_pred = reg.predict(X_test) # vector of predictions of dependent variable

(reg.intercept_,reg.coef_)

(13311.00883470787, array([5361.78229353]))

# Visualizing the Training set results
plt.scatter(X_train, y_train,color = 'red') # plot real values
plt.plot(X_train, reg.predict(X_train), color = 'blue') # plot regression line of predicted values on training set
plt.title('Salary vs Experience (Training set)')
plt.xlabel('Years of Experience')
plt.ylabel('Salary')
plt.show()

# Visualizing the Test set results
plt.scatter(X_test, y_test, color = 'red') # plot real values of test set
plt.plot(X_train, reg.predict(X_train), color = 'blue') # plot predicted values of test set # Same regression line as above
plt.title('Salary vs Experience (Test Set)')
plt.xlabel('Years of Experience')
plt.ylabel('Salary')
plt.show()

# Evaluate results
from sklearn import metrics

# Calculate metrics
print('MAE',metrics.mean_absolute_error(y_test, y_pred)) #MAE is the easiest to understand, because it's the average error
print('MSE',metrics.mean_squared_error(y_test, y_pred)) #MSE is more popular than MAE, because MSE "punishes" larger errors, which tends to be useful in the real world
print('RMSE',np.sqrt(metrics.mean_squared_error(y_test, y_pred))) #RMSE is even more popular than MSE, because RMSE is interpretable in the "y" units (target units)

MAE 5653.761026635242
MSE 55105733.870278984
RMSE 7423.3236404106065

##Calculated R Squared
print('R^2 =',metrics.explained_variance_score(y_test,y_pred))

R^2 = 0.9829807213710279