- m = Number of training examples.
- x = "input" variable / feature.
- y = "output" variable / "target" variable.
Hypothesis
$$ h_{\theta} (x) = \theta_0 + \theta_1 x$$
Parameters
$$ \theta_0, \theta_1$$
CostFunction
$$J (\theta_0, \theta_1) = \frac{1}{2 m} \sum_{i = 1}^{m_{}} (h_{\theta}
(x^{(i)}) - y^{(i)})^2$$
Goal
$$\underset{\theta_0, \theta_1}{minimize} J (\theta_0, \theta_1)$$
Gradient Descent
$$\begin{array}{lll}
\theta_j & = & \theta_j - \alpha \frac{\partial}{\partial \theta_j} J
(\theta_0, \theta_1) (for j = 0 and j = 1)
\end{array}$$
$$\begin{array}{lll}
temp_0 & = & \theta_0 - \alpha \frac{d}{d \theta_0} J (\theta_0,
\theta_1)\\
temp_1 & = & \theta_1 - \alpha \frac{d}{d \theta_1} J (\theta_0,
\theta_1)\\
\theta_0 & = & temp_0\\
\theta_1 & = & temp_1
\end{array}$$