So that sigma 1 and

But taking, you know, this max minus min would be fine.

M aircraft engines being manufactured.

X subscript 1 X subscript 2 and so on to denote my, in this case, four features and I'm going to continue to use

You can think of this as defining an additional zero feature.

And obviously we want to apply this to the future x zero, because the future x zero is always equal to one, so it cannot have an average value of zero.

These comics are now going to the New York festival.

Other things you might try are to well maybe try a smaller set of features.

Previously this was the form of our hypothesis, where x was our single feature, but now that we have multiple features, we aren't going to use the simple representation any more.

So x2 subscript 3 is going to be equal to 2. Now that we have multiple features,

For example, your jaws might be worn or damaged

The numbers 1 and 1 aren't too important.

So, this might be a

lot of features, maybe a hundred different features of different houses.

She made me feel that there was nothing I wouldn't do for her.

We can also try adding polynomial features things like x2 square x2 square and product features x1, x2.

like it's maybe a good idea, because that is a

In fact, they are going to be order and cube such features and if any is 100 you can compute that, you end up with on the order of about 170,000 such cubic features and so including these higher auto polynomial features when your original feature set end is large this really dramatically blows up your feature space and this doesn't seem like a good way to come up with additional features with which to build none many classifiers when n is large.

Let's introduce a little bit more notation.

I to denote the input features of the I training example.

Or maybe you need to get additional features.

So now we have, you know, four features. We want to use these four features to predict why the price of the house.

In these settings, a useful thing to do is to scale the features.

And, asymptotically, the number of quadratic features grows roughly as order n squared, where n is the number of the original features,

There's one little difference which is that when we previously had only one feature, we would call that feature x(i) but now in our new notation we would of course call this x(i)_1 to denote our one feature.

In that case maybe we'll call these features x1, x2, x3, and x4.

I'm going to use lowercase n to denote the number of features.

And as we saw we can come up with quite a

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

linear regression that we developed, we have a single feature x, the size of the house, and we wanted to use that to predict why the price of the house and this was our form of our hypothesis.

X2 is going to be a vector of the features for my second training example.

And so a matrix is a block of numbers that lets me take all of my data, all of my x's.

More generally, when we're performing feature scaling, what we often want to do is get every feature into approximately a 1 to 1 range and concretely, your feature x0 is always equal to 1.

So including all the quadratic features doesn't seem

And you want to use that to predict the price of the houses.

That's always your skill in applying this algorithms.

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

But now imagine, what if we had not only the size of the house as a feature or as a variable of which to try to predict the price, but that we also knew the number of bedrooms, the number of house and the age of the home and years.

In both of these cases, you therefore wind up with features x1 and x2.

We'll talk about its advantages and disadvantages later. Second, we'll also talk about algorithms for learning with a larger number of features.

layer because this is where we input our features, x1 x2 x3.

So, that's already in that range, but you may end up dividing other features by different numbers to get them to this range.

So, simple logistic regression together with adding in maybe the quadratic or the cubic features

So putting everything together, here is our anomaly detection algorithm.

And so X2 here is going to be a vector 1416, 3, 2, 40 since those are my four features that I have to try to predict the price of the second house.