linear in theta

linear combination of parameters $\theta$

define multiple linear regression

OLS problem formulation

ordinary least squares (OLS)

用线性代数重写之 $$ \mathbb{\hat{Y}} = \mathbb{X}\theta $$

multiple linear regression model

MSE

$$ R(\theta) = \frac{1}{n}||\mathbb{Y}-\hat{\mathbb{Y}}||_2^2 $$

geometric derivation

lin alg review: orthogonality, span

$$ span(\mathbb{A})是一个由列向量组成的space $$ 正交

least squares estimate proof

performance: residuals, multiple R-squared

lec11.ipynb

$$ R^2∈[0,1] $$ 越大拟合效果越好

OLS properties

residuals

the bias/intercept term

existence of a unique solution