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)'

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

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?