# Simple Linear Regression

#### Latest posts by Renuka Joshi (see all)

- Image Classification Using CNN - May 13, 2018
- Convolutional Neural Networks - May 12, 2018
- Hierarchical Clustering - March 15, 2018

# Simple Linear Regression

Hello all!Welcome to another brain storming tutorial for Machine Learning.In this article we are going to implement Simple Linear Regression using Python.

## Regression

Regression is an analysis of relationship between dependent and independent variables.It is a correlation between two variables.Regression analysis helps to understand how the value of a dependent variable changes when any of the values of independent variable varies.

## Types of Regression

Types of regression are as follows :

- Simple Linear Regression
- Multiple Linear Regression
- Polynomial Regression
- Support Vector for Regression(SVR)
- Decision Tree Classification
- Random Forest Classification

In this tutorial we are going to implement Simple Linear Regression using Python.So,Let’s get started.

## Simple Linear Regression

Simple linear regression determines the relationship between dependent and independent variables.It is a statistical analysis which predicts values of dependent variables based on the values of the independent variables.

Consider equation of a straight line,

y = c + mx

- where y is the dependent variable
- c is a constant,
- x is independent variable
- m is an coefficient i.e. slope of the line.

.

We are going to use LinearRegression class from sklearn.linear_model library.To implement simple linear regression we are going to create a new dataset containing at least 30 records of year of experience and total salary as follows.

YearsExperience,Salary

1.1,39343.00

1.3,46205.00

1.5,37731.00

2.0,43525.00

2.2,39891.00

2.9,56642.00

3.0,60150.00

3.2,54445.00

3.2,64445.00

3.7,57189.00

3.9,63218.00

4.0,55794.00

4.0,56957.00

4.1,57081.00

4.5,61111.00

4.9,67938.00

5.1,66029.00

5.3,83088.00

5.9,81363.00

6.0,93940.00

6.8,91738.00

7.1,98273.00

7.9,101302.00

8.2,113812.00

8.7,109431.00

9.0,105582.00

9.5,116969.00

9.6,112635.00

10.3,122391.00

10.5,121872.00

Preprocess the dataset and also divide the dataset into train and test dataset as follows.

1 2 3 4 5 6 7 8 9 10 11 12 13 |
# 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) |

- x_train : training data of independent variables. i.e. years of experience
- x_test : test data for which we want to predict salaries
- y_train : training data o dependent variables i.e. salaries based on years of experience
- y_test : actual salaries for years of experience in x_test

variables are as below. Please note x_train and y_train contain 20 values.

We are to fit our training dataset into simple linear regression model.To do this create an object **regressor** of class **LinearRegression**. Fit training data i.e. x_train and y_train in regressor as below.

1 2 3 |
from sklearn.linear_model import LinearRegression regressor = LinearRegression() regressor.fit(X_train, y_train) |

regressor.fit() method takes dependent and independent variables as parameters. We are actually teaching the regressor that y_train values are all corresponding to X_train values.

### Predicting salaries

We are now going to predict the salaries related to X_test values i.e years of experience and compare them with actual i.e values of y_test as below.

1 2 |
# Predicting the Test set results y_pred = regressor.predict(X_test) |

regressor.predict() method predicts the values of salaries depending on the years of experience in X_test.

y_pred values are predicted salaries and we will compare them with actual salaries which we have in y_test.

Image besides shows years of experience, predicted salaries and actual salaries.

- Regressor has predicted 40835.1 salary for an employee with 1.5 years of experience whose actual salary is 37731.
- Regressor has predicted 123079 salary for an employee with 10.3 experience whose actual salary is 122391

Here,machine has learned to predict the salaries based on years of experiences.

## Simple Linear Regression Graph:

### Training Set

1 2 3 4 5 6 7 |
# 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() |

- plt.scatter(X_train, y_train , color = 'red') plots scatter graph of salaries against years of experience for values in X_train and y_train
- plt.plot(X_train, regressor.predict(X_train), color = 'blue') plots the graph of predicted salaries against years of experience.
- Red dots represents co-relation between X_train and y_train i.e salaries and years of experience
- Blue line is the simple linear regression.

### Test Set:

1 2 3 4 5 6 7 |
# 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() |

plt.scatter(X_test, y_test , color = 'red') plots scatter graph of salaries against years of experience for values in X_test and y_test.

Please note that blue regression line remains the same as it shows all predicted salaries for any years of experience.

From the graph and our comparison of y_pred and y_test we can say that we have successfully predicted salaries for any given number of years of experience using Simple Linear Regression using python.

I hope this article helped understand Simple Linear Regression. In next article we will learn about multiple linear regression.

Pingback:Multiple Linear Regression - theJavaGeek

Mam.. Why to publish copied content as your own? I see most of the articles are copied from some other place. Put your genuine stuff.

Mam.. I found most of these articles at some other place.

Mam I have learned from udemy and wrote my own article, even I have provided references for same. Could you please share the link where do you find same stuff?

Pingback:Backward Elimination for multiple linear regression - theJavaGeek

Pingback:PyCharm for Machine Learning - theJavaGeek