low order polynomial such as a plus one, when we really needed a higher order polynomial to fit the data.

And I don't know exactly what this third degree polynomial

Now a third degree polynomial can have as many as three 0's.

They say it's a third degree polynomial of the form ax to the third plus bx squared plus cx plus d.

look at how well my fifth order polynomial hypothesis, had done on my test set.

In order to get the third dimension, redshifts are needed.

In that case, given that we're fitting a high order polynomial, this is a usual overfitting setting.

So this one must have a third real 0, because if the third one was complex, you'd need another complex 0, and you can't have four 0's for a third degree polynomial.

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

In order to activate the third eye we are going to reverse this process.

line to the data, we might decide that it's better to fit a quadratic function or a second order polynomial to this data.

I have this polynomial in the denominator here.

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

Let's say I'm defining, so this is a polynomial.

So for this example, let's say for the sake of argument that it was my fourth order polynomial that had the lowest cross validation error.

So in that case, I'm going to pick this fourth order polynomial model and finally what this means is that that parameter d, remember d was the degree of polynomial, right d equals 2, d equals 3, up to d equals 10.

Suppose we fit a linear regression model with a very high order polynomial, but to prevent overfitting, we are going to use regularization as shown here.

So a binomial is just a polynomial with two terms.

Mis order! Order!

So the first thing is to think about, is what would a third degree polynomial look like and what are we even talking about when we say 0's.

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.

I've chosen the degree d of polynomial using the test set.

And this polynomial we're going to do, we're going to keep adding terms to the polynomial, so that we can better and better approximate this function.

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