**The two basic types of regression**

1.Linear regression and Non Linear

2.Multiple regressions

The general form of regression is :

Linear regression: $Y=m+n X+u$

Multiple regression: $Y=m+n_{1} X_{1}+n_{2} X_{2}+n_{3} X_{3}+\ldots+n_{1} X_{t}+u$

$\mathrm{Y}=$ The dependent variable which we are trying to predict

$\mathrm{X}=$ The independent variable that we are using to predict variable $\mathrm{Y}$

$\begin{aligned} \mathrm{m} &=\text { The intercept } \\ \mathrm{n} &=\text { The slope } \\ \mathrm{y} &=\text { The regression residual. } \end{aligned}$

**Linear Regression:**
Regression tries to find the mathematical relationship between variables, if it is a straight
line then it is a linear model and if it gives a curved line then it is a non linear model.

**Non-Linear Regression:**

Nonlinear regression uses nonlinear regression equations, which take the form: $Y=f(X, \beta)+\varepsilon$

Where,

$X=a$ vector of **p** predictors,

$\beta=a$ vector of **k** parameters,

$f(-)=$ a known regression function,

$\varepsilon=$ an error term.

**Multiple linear regression:** Multiple linear regression is an extension of simple linear regression analysis.
It uses two or more independent variables to predict the outcome and a single continuous
dependent variable

$Y=a_{0}+a_{1} X_{1}+a_{2} X_{2}+\ldots+a_{k} X_{k}+e$

Where,

$\quad \mathrm{Y}$ is the dependent variable or response variable

$\mathbf{X}_{1}, \mathbf{X}_{2} \ldots \ldots \ldots . \mathbf{X}_{\mathbf{k}}$ are the independent variables or predictors

e is random error.

$a_0, a_{1}, a_{2} \ldots \ldots a_{k}$ are the regression coefficients