Mathematics of Ridge regression

Let's get started with "What do we have to do?"

In such case of simple linear regression(OLS).b=y_mean-m*x_mean and m=∑(Xi-X_mean)(yi-y_mean)/∑(Xi-X_mean)²

^{In such a case of ridge we derive everything again but we don't derive b because in ridge we reduce m not b will be the same as well.}

1. Choose a loss function.In this case I choose L=𝜮(yi-p)²

2. Calculate dL/dm=∑(Xi-X_mean)(yi-y_mean)/∑(Xi-X_mean)²+λ to minimize loss

Then m=∑(Xi-X_mean)(yi-y_mean)/∑(Xi-X_mean)²+λ

And in this case, you clearly see if we increase λ m decrease but it affects b also but not that much

And λ is a hyperparameter in whole Regularization

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