The chart below show 30 examples in three classes—red, green, and blue. Each class has two inputs $x_1$ and $x_2$ that range between 0 and 100.

The Julia program below finds polynomial logistic models for the classes. It uses gradient descent to find $\theta_0^{(i)}, \theta_1^{(i)}, ... \theta_4^{(i)}$ for $i = {1, 2, 3}$.

The above program should run in under a minute and then print out $\theta$ values. For each of the classes, try entering its $\theta$ values below. When you’ve entered all the values, you will see what the model function for that class looks like.

 $$\theta_0$$ $$\theta_1$$ $$\theta_2$$ $$\theta_3$$ $$\theta_4$$