We have a function to find the gradient of b at every point. To find the m gradient, or the way the loss changes as the slope of our line changes, we can use this formula:
Once more:
Nis the number of points you have in your datasetmis the current gradient guessbis the current intercept guess
To find the m gradient:
- we find the sum of
x_value * (y_value - (m*x_value + b))for all they_values andx_values we have - and then we multiply the sum by a factor of
-2/N.Nis the number of points we have.
Once we have a way to calculate both the m gradient and the b gradient, we’ll be able to follow both of those gradients downwards to the point of lowest loss for both the m value and the b value. Then, we’ll have the best m and the best b to fit our data!
Instructions
Define a function called get_gradient_at_m() that takes in a set of x values, x, a set of y values, y, a slope m, and an intercept value b.
For now, have it return m.
In this function, we want to go through all of the x values and all of the y values and compute x*(y - (m*x+b)) for each of them.
Create a variable called diff that has the sum of all of these values, and return it from the function.
Define a variable called m_gradient and set it equal to the -2/N multiplied by diff.
Instead of returning diff, return m_gradient.