# What is the difference between a simple and multiple regression?

Oct 30, 2015

The number of explanatory variables

#### Explanation:

Let's take the example of the linear regression.
A simple linear regression model has the form :

$Y = a X + b + e$

With
-Y the response variable (the one you want to explain)
-X the explanatory variable (with which you want to explain Y)
- a the slope
- b the intercept
- e the residuals (the variance not explained by the linear regression)

In the case of a multiple linear regression, you have more than one explanatory variable :

$Y = {a}_{1} {X}_{1} + {a}_{2} {X}_{2} + b + e$

It is practical in the way that you can use only one model with several variables (X) to explain an other one (Y). For example, the number of grains on corn (Y) explained by the type of soil (X1) and the amount of water (X2).
Be cautious if you want to make predictions with this kind of model. You have to keep one one of the explanatory variables fixed. For example, on a clay soil, how the number of grain varies with the amount of water.