**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-

- Simple Linear Regression
- 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 = β _{0} + β_{1}X**

Here,

- Y is a dependent variable.
- X is an independent variable.
- β
_{0}and β_{1}are the regression coefficients. - β
_{0}is the intercept or the bias that fixes the offset to a line. - β
_{1}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: β**_{1} < 0

_{1}< 0

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

**Case-02: β**_{1} = 0

_{1}= 0

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

**Case-03: β**_{1} > 0

_{1}> 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 = β _{0} + β_{1}X_{1} + β_{2}X_{2} + β_{3}X_{3} + …… + β_{n}X_{n}**

Here,

- Y is a dependent variable.
- X
_{1}, X_{2}, …., X_{n}are independent variables. - β
_{0}, β_{1},…, 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.

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