Simple Linear Regression

Basics:

Here is how Linear Regression (LR) is defined in mathematics:
Coefficient is also defined as 'Slope'. More the slope, more the hike in salary.

Ordinary Least Square (OLS):

LR applies OLS method to find the trend line.
Here Red denotes the current value (y) and Green denotes Ideal/Model value (y hat).
Using OLS method, LR draws various trend lines and records the sum of difference between the two points, as shown. Eventually it keeps the minimum out of all findings, describing the best fitting line.

Code Snippet: Simple Linear Regression

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

# Importing the dataset
dataset = pd.read_csv('Salary_Data.csv')
X = dataset.iloc[:, :-1].values
y = dataset.iloc[:, 1].values

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

# Fitting Simple Linear Regression to the Training set
from sklearn.linear_model import LinearRegression
regressor = LinearRegression()
regressor.fit(X_train, y_train)

# Predicting the Test set results  (Not Used Anywhere)
y_pred = regressor.predict(X_test)

# Visualising the Training set results
plt.scatter(X_train, y_train, color = 'red')
plt.plot(X_train, regressor.predict(X_train), color = 'blue')
plt.title('Salary vs Experience (Training set)')
plt.xlabel('Years of Experience')
plt.ylabel('Salary')
plt.show()

# Visualising the Test set results
plt.scatter(X_test, y_test, color = 'red')
plt.plot(X_train, regressor.predict(X_train), color = 'blue')
plt.title('Salary vs Experience (Test set)')
plt.xlabel('Years of Experience')
plt.ylabel('Salary')
plt.show()

Hope this helps !!!

Arun Manglick