Here's our linear separation classification function where this is our common linear function.

They ask us, is this function linear or non linear?

So it's a nice linear function.

It's just a linear function asymptotically.

The derivative of a quadratic function is a linear function.

That's why it's called a linear function.

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

If they're not, then we're dealing with a non linear function.

And why a linear function? Well, sometimes we'll want to fit more complicated, perhaps non linear functions as well.

A function is linear if each resulting pixel of the processed image is a linear combination of input pixels.

Maybe it's a cost function from linear regression. Maybe it's some other function we want to minimize.

You can see I did a, the LM function for Linear Model.

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.

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

Let F of XP, or linear function, and the output of logistic regression is obtained by the following function

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

The slope of a linear function, is just rise over run. Remember that?

It looks like it's a linear function so far, but actually it diverges now.

This is also non linear, because I multiplied the function times its second derivative.

To see, let's look at the slope of the linear function if it existed.

But, it turns out that the cost function for gradient of cost function for linear regression is always going to be a bow shaped function like this.

Again LM is the function in R, stands for linear model. Uh, you do one.

If it's always going to be the same value, you're dealing with a linear function.

Linear

linear

Linear

Linear

Linear

In the next video, we're going to take the function J, and set that back to be exactly linear regression's cost function.

There are a lot of examples from psychology where you get this quadratic function between two variables, rather than a linear function.

In our linear case, we have L equals sum over the correct labels minus our linear function to the square, which we seek to minimize.

The word is called here, are loss function and the loss function is the amount of residual error we obtain after fitting the linear function as good as possible.

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

We actually plotted the running time, and it really did give a very nice linear function.

And the form of the hypothesis, which we use to make predictions, is this linear function.

Today's negative correlation but it's weak. The data really in't well described by a linear function.

What is the range in which Z might fall given this function over here, and ??? the linear function of F or X over here.

Linear Spline

Linear Sweep

Random Linear

Linear motion

Y linear

Linear B

Linear Scale

Bi Linear