In this particular example, it

Clearly a linear regression model is a very poor one to explain this data over here.

Let's look at some examples.

So, this term here.

So why do we need yet another learning algorithm?

You know, you can end up here or here.

In the original version of

Y is either zero or one, but if you are using

And I'll quickly review the linear algebra you need in order to implement and use the more powerful versions of linear regression.

Tropic of Cancer

Tropic of Capricorn

And taking gradient descent, and the square cost function, and putting them together. That will give us our first

There is really no residual error over here.

And, just to give this another name, this is also called multivariate linear regression.

For such situations there is a model called logistic regression, which uses a slightly more complicated model than linear regression, which goes as follows .

linear regression.

But somehow adding that example out there caused linear regression to change in straight line fit to the data from this magenta line out here to this blue line over here, and caused it to give us a worse hypothesis.

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.

In this video, let's talk about how to fit the parameters of that hypothesis.

Thrun It's interesting to see how to minimize a loss function using gradient descent.

Now we plug in W1 0.9 4 x 20 equals 0.5.

So here's a quick quiz for you.

First what I'd like to show you is just, what do I mean by linear and nonlinear.

But if you implement the algorithm written up here then you have a working implementation of linear regression with multiple features.

Once again, we're looking for function f that maps our vector x into y.

The line of 25.2 0.67x y.

That minimizes J of theta one.

In the first instance, in the first example before I added this extra training example, previously linear regression was just getting lucky and it got us a hypothesis that, you know, worked well for that particular example, but usually apply

Let's for now just consider the one dimensional case.

So in this video, I'm going to talk about gradient descent for minimizing some arbitrary function J. And then in

Because if you are minimizing quadratic error, outliers penalize you over proportionately.

They move they go up, they go down.

So, using a vectorized implementation, you should be able to get a much more efficient implementation of linear regression.

Now, there are many different ways to apply linear functions in machine learning.

So let's dive straight in so let's talk about lines and let's talk about the technology to fit lines to data called linear regression.

So, sometimes we use linear regression with tens or hundreds thousands of features, but if you use the vectorized implementation of linear regression, usually that will run much faster than if you had say your old for loop that was you know, updating theta 0 then theta 1 then theta 2 yourself.

If you want to apply logistic regression to this problem, one thing you could do is apply

Therefore, 4b 1 and then we divided by 4, which means b equals to fourth or quarter and 0.25 and 1 other correct answers here.

And words, it just means.

We'll be able in the next few videos to develop more powerful forms of linear regression that can view of a lot more data, a lot more features, a lot more training examples and later on after the new regression we'll actually continue using these linear algebra tools to derive more powerful learning algorithims as well

Let me also give this particular model a name.

I've drawn the blue box around.

liter

linear

lightyears