Linear Regression-

 

In Machine Learning,

• Linear Regression is a supervised machine learning algorithm.
• It tries to find out the best linear relationship that describes the data you have.
• It assumes that there exists a linear relationship between a dependent variable and independent variable(s).
• The value of the dependent variable of a linear regression model is a continuous value i.e. real numbers.

 

Also Read- Machine Learning Algorithms

 

Representing Linear Regression Model-

 

Linear regression model represents the linear relationship between a dependent variable and independent variable(s) via a sloped straight line.

 

 

The sloped straight line representing the linear relationship that fits the given data best is called as a regression line.

It is also called as best fit line.

 

Types of Linear Regression-

 

Based on the number of independent variables, there are two types of linear regression-

 

 

1. Simple Linear Regression
2. Multiple Linear Regression

 

1. Simple Linear Regression-

 

In simple linear regression, the dependent variable depends only on a single independent variable.

 

For simple linear regression, the form of the model is-

Y = β₀ + β₁X

 

Here,

• Y is a dependent variable.
• X is an independent variable.
• β₀ and β₁ are the regression coefficients.
• β₀ is the intercept or the bias that fixes the offset to a line.
• β₁ is the slope or weight that specifies the factor by which X has an impact on Y.

 

There are following 3 cases possible-

 

Case-01: β₁ < 0

 

• It indicates that variable X has negative impact on Y.
• If X increases, Y will decrease and vice-versa.

 

 

Case-02: β₁ = 0

 

• It indicates that variable X has no impact on Y.
• If X changes, there will be no change in Y.

 

 

Case-03: β₁ > 0

 

• It indicates that variable X has positive impact on Y.
• If X increases, Y will increase and vice-versa.

 

 

2. Multiple Linear Regression-

 

In multiple linear regression, the dependent variable depends on more than one independent variables.

 

For multiple linear regression, the form of the model is-

Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + …… + β_nX_n

 

Here,

• Y is a dependent variable.
• X₁, X₂, …., X_n are independent variables.
• β₀, β₁,…, β_n are the regression coefficients.
• β_j (1<=j<=n) is the slope or weight that specifies the factor by which X_j has an impact on Y.

 

To gain better understanding about Linear Regression,

Watch this Video Lecture

 

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