The problem with Linear Regression

Before defining the Polynomial Regression, let's look at the case that the Linear Regression we learned doesn't handle well.

Here you can see that our simple linear regression model is doing awful. It tries to fit a straight line to the data points.
Yet we can see that fitting a parabola would be a much better choice for our points.

Quadratic Regression Equation

To build a straight-line model, we used an equation of a line (y=ax+b).
So to build a parabolic model, we need the equation of a parabola. That is the quadratic equation: y=ax²+bx+c.
Changing the a, b, and c to β would give us the Quadratic Regression Equation:

The model this equation describes is called Quadratic Regression.
Like before, we only need to find the best parameters for our data points.
The following gif shows how changing each parameter modifies the regression line.

Although, we are not only limited to a Quadratic Regression. Let's move to the next chapter, where you will learn about Polynomial Regression in general.