Linear Regression

Machine Learning: Start with linear regression

“a very simple approach for supervised learning”

“widely used statistical learning method”

House Prices

Square feet | Price

$y = Mx + b$

Written as $y = \beta_0 + \beta_1x$

y is called response or target x predictor

Once we know betas we can predict value of response

Minimize the total error from each point to our line.

Bend the line to fit better

Square feet | # bedrooms | Price

cs229 Example

Simple Linear one variable

“We typically assume that the error term is independent of X.”

p71

We usually have more than one predictor.

$Y = \beta_0 + \beta_1 X_1 + \cdots + \beta_p X_p + \epsilon$

p72

$\hat{y} = \hat{\beta}_0 + \beta_1 X_1 + \cdots + \beta_p X_p + \epsilon$

RSS =

Choose $\beta$ to $\beta_p$ that minimizes RSS p73