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?