Challenge: Fitting a Line with Gradient Descent

A student wants to use gradient descent to fit a straight line to a dataset showing years of experience versus salary (in thousands). The goal is to find the best-fitting line by adjusting the slope ($m$) and intercept ($b$) using iterative updates.

You need to minimize the loss function:

The gradient descent update rules are:

Where:

• $\alpha$ is the learning rate (step size);
• $\frac{\raisebox{1pt}{$\partial J$}}{\raisebox{-1pt}{$\partial m$}}$ is the partial derivative of the loss function with respect to $m$;
• $\frac{\raisebox{1pt}{$\partial J$}}{\raisebox{-1pt}{$\partial b$}}$ is the partial derivative of the loss function with respect to $b$.

Your task:

1. Complete the Python code below to implement the gradient descent steps.
2. Fill in missing expressions using basic Python operations.
3. Track how m and b change as the algorithm runs.