That's because I've fit my parameters to the test set.

So they give us a function, f of x.

So let me just draw a little bit of a graph.

So the easiest way to approximate it is to say, well, the simplest polynomial is just a constant, right?

So x is equal to r3.

For example, instead of sending a straight

Now let's consider the model selection problem.

Let's start with the training error.

lambda, such as if lambda were equal to 0.

In this video, I want to focus on a few more techniques for factoring polynomials.

Polynom

polynom

So let's see if we can make some headway on this.

So, you should you choose a linear function, a quadratic function, a cubic function, all the way up to a 10th power polynomial?

Sometimes there's more than one, right?

Now let's plot the following figure.

One thing I could do is

And the reason is, what we've done is, we've fit this extra the parameter d, that is this degree of polynomial, and we'll fit that parameter d using the test set.

So if we viewed a squared as kind of the independent variable or the x term, so now this kind of has the shape of polynomials that hopefully you're used to factoring a

Consider the following graph where the horizontal axis graphs complexity of the solution.

So that's the area and it's a monomial.

Now let's try another expression.

So let's try to factor each of them. So first, let's try the numerator. And I'll actually do it up here.

In this video I want to do a bunch of examples of factoring a second degree polynomial, which is often called a quadratic.

Let me draw my axes.

And what we did in this with the repeated factor is true if we went to a higher degree term.

What can I do with this?

That's y minus 1 squared.

How many times does x minus 2 go into 2x squared minus 8?

So let's add our x terms.

whereas we're here on the right of the horizontal axis, I have much larger values of these of a much higher degree polynomial, and so here that is going to correspond to fitting much more complex functions to your training set.

The y terms become 4 times y minus 2 squared. y minus 2 squared.

Let's do another one like this.

And we showed it in the beginning.

No need to feed me or recharge me.

Let's say this is my polynomial, let me call my polynomial p of x.

So when you see something like this, when the coefficient on the x squared term, or the leading coefficient on this quadratic is a 1, you can just say, all right, what two numbers add up to this coefficient right here?

Whereas in contrast, this regime corresponds to a high variance problem.

So this checks out.

I have something shifted here.

So this first degree so this is going to be a 0 degree or a constant term Here the degree is 2.

This b over here is different than the b that we are using in the equation.

And let's say, for the sake of this example, that I end up picking theta 5, the fifth order polynomial, because that has the Noah's cross validation error.

In this case, in all of the examples we'll do, it'll be x.

Sometimes a quadratic polynomial, or just a quadratic itself, or quadratic expression, but all it means is a second degree polynomial.