Regression Analysis

Definition: discovering correlations between the outcome $y$ and the set of regressors $x$ (features)

$y$ : real random variable
$x$ : vector or random variables $X=(X_1,...,X_p)'$

Example
For wages, suppose
$y$ : hourly wage
$x$ : regressors (experience, gender, education)

$X=(D,W')'$
$D$ : target regressor
$W$ : controls of components

Prediction: how can we use $X$ to predict $Y$ well?
Inference: how does the predicted value of $Y$ change if we change a component of $X$ holding the rest of the components of $X$ fixed?