Multiple Linear Regression From Scratch Compute Prediction $f_{\vec{w},b}(X) = \vec{w} \cdot X + b$ Compute Cost Function $J(\vec{w},b) = \frac{1}{2m} \sum_{i=0}^{m} (f_{\vec{w},b}(\vec{x}^{(i)}) - y^{(i)})^2 $ Compute Gradient of Cost $\frac{\partial J}{\partial \vec{w}} = \frac{1}{m} X^T \cdot (f_{\vec{w},b}(X) - Y)$ $\frac{\partial J}{\partial b} = \frac{1}{m} (f_{\vec{w},b}(X) - Y)$ Gradient Descent for $w_j$ = {1...n} $w_j := w_j - \alpha \frac{\partial J}{\partial \vec{w}}$ $b := b - \alpha \frac{\partial J}{\partial b}$