So far, we have looked at linear regression with only one feature. It is called simple linear regression. But in reality, most of the time target depends on multiple features. Linear regression with more than one feature is called Multiple Linear Regression

Two-Feature Linear Regression Equation

In our example with heights, adding the mother's height as a feature to the model would likely improve our predictions. But how do we add a new feature to the model? An equation defines linear regression, so we just need to add a new feature to an equation:

Where:

• $\beta_0, \beta_1, \beta_2$ – are the model's parameters;
• $y_{\text{pred}}$ – is the prediction of a target;
• $x_1$ – is the first feature value;
• $x_2$ – is the second feature value.

Visualization

When we discussed the simple regression model, we built the 2D plot where one axis is the feature, and the other is the target. Now that we have two features, we need two axes for features and the third one for the target. So we are moving from a 2D space to a 3D one, which is much harder to visualize. The video shows a 3D scatterplot of the dataset in our example.

But now, our equation is not an equation of a line. It is an equation of a plane. Here is a scatterplot along with the predicted plane.

You may have noticed that mathematically our equation hasn't become much harder. But unfortunately, the visualization has.