## STATISTICS Course

# Explanations about the equation

We will explain the following equation of regression:

@ Y = a + b X + residual @

$Y$ is a quantitative variable, called response/dependent variable or `variable à expliquer/réponse/cible`

.

$X$ is a variable (either qualitative or quantitative) called explanatory/predictor variables or `variable explicative/prédicteurs/facteur (rare)`

.

$a$ is called the intercept coefficient/`coefficient d’interception`

.

$b$ is the coefficient of $X$.

The $residual$, also called noise or $\epsilon$, is a measure of the error.

**Note**: if you want $Y$ to be qualitative, then you should look at Linear discriminant analysis (analyse factorielle discriminante) or at Random forest (Arbres de Décision et Forêts Aléatoires).

## Simple/Multiple

Since we only have one variable ($X$) is called "simple linear/logistic regression" but if you have something like $Y = a + b X + c Y + ... + residual$ then you will have to deal with "multiple linear/logistic regression".

## And what's the goal?

What we are trying to observe using a regression model, is the dependency between $Y$ and the predictor variables.

The result is a model, presented as a table, in which you will have the dependency between the predictor variables and Y. You will be able to see the estimated impact of a variable on Y, for each predictor variable.

You could also use your model to make predictions.