Course Content

# Linear Regression with Python

4. Choosing The Best Model

Linear Regression with Python

## Linear Regression With n Features

## n-feature Linear Regression Equation

As we have seen, adding the new feature to the linear regression model is as easy as adding it along with the new parameter to the model's equation. We can add much more than two parameters that way.

Note

Consider

nto be a whole number greater than two.

## Normal Equation

The only problem is the visualization. If we have two parameters, we need to build a 3D plot. But if we have more than two parameters, the plot will be more than three-dimensional. But we live in a 3-dimensional world and cannot imagine higher-dimensional plots. However, it is not necessary to visualize the result. We only need to find the parameters for the model to work. Luckily, it is relatively easy to find them. The good old Normal Equation will help us:

## X̃ Matrix

Notice that only the **X̃** matrix has changed. Let's take a closer look at this matrix. You can think of the columns of this matrix as each responsible for its **β** parameter. The following video explains what I mean.

The first column of 1s is needed to find the **β₀** parameter.

Everything was clear?

Course Content

# Linear Regression with Python

4. Choosing The Best Model

Linear Regression with Python

## Linear Regression With n Features

## n-feature Linear Regression Equation

As we have seen, adding the new feature to the linear regression model is as easy as adding it along with the new parameter to the model's equation. We can add much more than two parameters that way.

Note

Consider

nto be a whole number greater than two.

## Normal Equation

The only problem is the visualization. If we have two parameters, we need to build a 3D plot. But if we have more than two parameters, the plot will be more than three-dimensional. But we live in a 3-dimensional world and cannot imagine higher-dimensional plots. However, it is not necessary to visualize the result. We only need to find the parameters for the model to work. Luckily, it is relatively easy to find them. The good old Normal Equation will help us:

## X̃ Matrix

Notice that only the **X̃** matrix has changed. Let's take a closer look at this matrix. You can think of the columns of this matrix as each responsible for its **β** parameter. The following video explains what I mean.

The first column of 1s is needed to find the **β₀** parameter.

Everything was clear?