Hello! Today, we're going to talk about Ridge Regression. Ridge Regression is a special type of linear regression that helps when we have too many features (or variables) in our data. Imagine you have a lot of different ingredients for a recipe but don't know which ones are essential. Ridge Regression helps us decide which ingredients (or features) are important without overloading the recipe.

In this lesson, we'll learn:

1. What Ridge Regression is.
2. How to use Ridge Regression in Python.
3. How to interpret the results.
4. How Ridge Regression compares to regular linear regression.

Ready to dive in? Let's go!

Ridge Regression is like normal linear regression but with a regularization term added. Why do we need this?

Think about building a sandcastle. If you pile up too much sand without structure, it might collapse. Similarly, in regression, too many variables can make our model too complex and perform poorly on new data. This is known as overfitting.

Ridge Regression helps by adding a "penalty" to the equation that keeps the coefficients (weights assigned to each feature) smaller. This penalty term is controlled by a parameter called $\alpha$.

This penalty works by adding the sum of the squared values of the coefficients to the cost function. In mathematical terms, the Ridge Regression cost function is:

$J(\theta$