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