linear regression.

linear regression for fitting a straight line to our data.

This line over here is linear regression to the data.

So, that's linear regression.

linear regression for classification problems.

Then linear regression tries to fit a line that best describes the data.

So, here's our linear regression algorithm.

linear regression isn't a good idea .

So linear regression works well if the data is approximately linear, but there are many examples when linear regression performs poorly.

So that's linear regression with gradient descent.

And thus, using linear regression this way.

Linear regression? Do we compute confidence intervals?

So outliers are particularly bad for linear regression.

Our first learning algorithm will be linear regression.

You now know about linear regression and gradient descent.

And let's say you've implement and regularize linear regression.

This model is called linear regression or this, for example, is actually linear regression with one variable, with the variable being x.

Thrun In this question I quiz you about linear regression.

Right? This was our objective function for the linear regression.

line intercept plus slope, and that's simple regression.

We already have linear regression and we have logistic regression, so why do we need, you know, neural networks?

Are there closed form solutions of the type we found for linear regression?

So this is going to be my overall objective function for linear regression.

Up to this point, I've just been showing you linear relationships, this regression

The minimizing of loss is used for linear regression of a new regression problem, and you can write it as follows

That's our gradient descent algorithm, which should be familiar, and you see the linear linear regression model with our linear hypothesis and our squared error cost function.

To define linear regression, we need to understand what we are trying to minimize.

And this seems a pretty bad thing for linear regression to have done, right?

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

But once we've added that extra example out here, if you now run linear regression, you instead get a straight line fit to the data.

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

Right? Doesn't mean that they are right on the regression line.

It doesn't mean that everyone is right on the regression line.

And you can see the regression line in the scatter plot.

We can calculate it, for. A slope, of a regression line.

Here's a usual hypothesis of linear regression and if you want to compute H of

So, applying linear regression to a classification problem usually isn't, often isn't a great idea.

They seem to line up a little bit in linear fashion.

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

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.

In linear regression, the function has a particular form which is W1 times X plus W0.

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

In particular let's talk about how to use gradient descent for linear regression with multiple features.

For linear regression, we compute the quotation B and A, and I give you the formulas

In linear regression, we are given data and data has still has more than one dimension.