The coefficient of the independent variable is equal to -0,0127

The coefficient of the independent variable is equal to 84,41

The coefficient of the independent variable is equal to 0,0180

The value of the independent term  is equal to 0,904

The value of the independent term is equal to -0,0127

The value of the independent term  is equal to 0,0180

We define the loss function (error between current predicted value and reality):

Replacing the predicted value with the formula of the estimation  we obtain

Now we define a Learning rate . It should be a small number, e.g. 0,01.

We start with two values for and . Suppose and .

At each step:

We calculate the partial derivative of the loss function with respect to , and replace the current values of to obtain the derivative value :

Similarly, we calculate the partial derivative with respect to , :

Now we update the current value of and using the equations

We repeat this process until the loss function is a very small value, or ideally 0. The final values of and are the optimum values.

Solving a minimization problem

from which we found the estimated values