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>> So the simple alternative approach is gradient descent.
Where, remember that the gradient descent algorithm,
we just initialize our vector of parameter somewhere and take these gradient steps.
And eventually, we will converge
to the optimum of this problem.
Okay, so what does this algorithm look like for multiple regression?
Well, it looks very similar to our simple linear regression,
where we say while not converged, we're gonna take our w parameters.
And we're gonna update them by subtracting sum step size atta times the gradient
of our residual sum of squares, at our previous set of parameters wt.
So what is our residual sum of squares?
Sorry, the gradient of the residual sum of squares, I'm writing right here,
so this update is w at iteration t.
The minus sign and this minus sign will turn into a plus sign.
Two eta times this h matrix,
h transpose y- Hw at iteration t.
And what is this here?
Well, h times w at iteration t is my predicted set of observations,
the whole vector of them.
Assuming that I use w at iteration t performing those predictions.
Okay, so what this version of the algorithm is doing is it's taking our
entire w vector, all the regression coefficients in our model, and
updating them all at once using this matrix notation shown here.
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