# What is Multiple Linear Regression?

Learn what is multiple linear regression with this simple tutorial explained with formula and an example.

## Multiple Regression Tutorial With Formula, Example

**What is Multiple Linear Regression?**

Multiple regression is an extension of linear regression. The multiple regression describes the **relationship between more than two variables**. The variables used in multiple regression is called as **predictor** and **response** **variable**.

**Multiple Regression Formula:**

Mathematical equation for multiple regression is defined as:

**y = a + b1x1 + b2x2 +...bnxn**

Where,

y is the response variable.

a, b1, b2...bn are the coefficients.

x1, x2, ...xn are the predictor variables.

The **lm() function**:

When you want to know the relationship model between the predictor and the response variable, the lm() function is used. The below syntax presents the ** relation between the response variable and predictor variables**. This function is most widely used to determine the value of the coefficients using the
input data, which is helpful in predicting the given
set of predictor variables using the below functions.

**lm() function Syntax:**

lm(y ̃ x1+x2+x3...,data)

**Example:**

**lm() function Example: **

Consider an R environment with the data set "mtcars". Use the dataset to compare between the different car models in terms of mileage per gallon (mpg), cylinder displacement ("disp"), horse power("hp"), weight of the car("wt") and some more parameters. Create a subset of these variables from the mtcars data set.

The below formula gives you the relationship between "mpg" as a response variable and "disp","hp" and "wt" as predictor variables.

input <- mtcars[,c("mpg","disp","hp","wt")]

print(head(input))

Result:

**Executing the program....**

$Rscript main.r

mpg disp hp wt
Suzuki SX4 21.0 170 128 2.647
Toyota Wag 21.0 170 129 2.871
Datsun Go+ 22.8 128 94 2.234
Tata Ecodrive 21.4 268 110 3.493
Honda City+ 18.7 160 147 3.593
Mahindra Scorpio 18.1 255 139 3.103

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