Linear Regression

Implement a simple linear regression model with MSE loss.

The model predicts: $\hat{y} = x \cdot w + b$

The MSE loss is: $L = \frac{1}{N} \sum (y - \hat{y})^2$

Input:

• x: input tensor of shape (N, 1)
• w: weight scalar of shape (1, 1)
• b: bias scalar of shape (1,)
• y: target values of shape (N, 1)

Output: A dict with “prediction” (shape (N, 1)) and “loss” (scalar).