STATISTICS Course

Explanations about the equation

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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.