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All right, my friends,

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here we are
at the final step of this implementation

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and actually the most exciting one,
because this is the step where

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we're going to visualize it
on a nice 2D plot, the prediction curve

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and the prediction
regions of the logistic regression model.

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All right.

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So more specifically,
what we're about to plot

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is a two dimensional plot with therefore

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two axes x and y on the x axis.

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You will have the first feature
corresponding to the h, and on the y axis

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you'll have the second feature
corresponding to the estimated salary,

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and therefore each of the observation
points you will see on the 2D

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plot will correspond
to a specific customer.

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It will either be a customer
of the training set.

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You know,
on the plot of the training set results,

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or a customer of the test
set on the plot of the test result.

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And what is most interesting to see in

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this plot will be the prediction regions,
meaning the regions

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where our logistic regression
model predicts the class zero,

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meaning the customers
didn't buy the SUV, and the other region

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where our logistic regression
model predicts the class one,

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meaning the customer, but the SUV.

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And lastly,
what will be really interesting to see

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is the curve separating these two regions.

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You know, the region of the prediction
zero and the region of the predictions

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one. And this is exactly how we are going
to see the difference

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between linear classifiers
and nonlinear classifiers.

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So here we only starting with one
classification model logistic regression.

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So we won't compare that yet.

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But you will see in the next sections
of this part that the prediction

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boundary between these two prediction
regions will be different

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depending on whether or not
your classifier is linear.

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All right.
So I can't wait to show you this.

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And let's start
first by visualizing these training

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set and test results
for the logistic regression model.

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All right.

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So the code to visualize
this is actually pretty advanced.

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And not only it is pretty advanced,
but also you will

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probably never use it again
in your career.

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Or let's say you will never have
to implement that again.

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Why is that?

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It's because in your career
you will mostly work

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with data sets, having many features,
you know, more than two.

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And here the only reason why
we have a data set of two features

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is so that we can be able to visualize
indeed, well, these prediction regions

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and prediction boundary,

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because indeed, in order to visualize
this, we need maximum two features,

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because one feature corresponds
to one dimension in this plot.

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So what I suggest is
that we don't waste too much time,

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you know, understanding the whole code
and re-implemented ourselves.

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Because really, I'm going
to show it to you right away, you know,

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on the original logistic regression
implementation,

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you will see that
the code is pretty advanced.

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You know, it's not like plotting a
regression curve like we did in part two.

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So that's the test results.

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Let me show you the training set results.

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All right.

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So that's the code.

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You see it's uses a lot of tricks
to plot all these observation points.

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Prediction regions
and prediction boundary.

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So if you want to have a look at it
and understand it fine.

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But really for the others it's totally
okay if we don't cover this code in detail

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because this is only for training
purposes.

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Just so that I can show you

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the differences between linear classifiers
and nonlinear classifiers,

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and you will probably never use that again
in your future machine learning project.

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However, what I will do
just now is explain how it's done.

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Basically, what we do is we create,
as you can see, a grid

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which is basically this frame here
containing all the edges of your features

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and all the estimated salaries,
you know, the ranges,

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and you create this grid
with a high density, meaning that

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the pixels of this grid are not separated
one by one, but every oh point 25.

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So here, for example, for the age,
it goes this way.

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It goes from 10 to 10.20 5
to 10.5 to 10.75 to 11, etcetera.

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Up to 69, 69.25, 69.5,

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69.75, 70 okay,
and same for the estimated salary.

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It goes from 20,000,
then 20,000.25, 20,000.5, etc.

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up to somewhere around 149,000 149,000.25.

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You see, so resulting in having super
dense points inside this grid

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and then the trick, you know, what we did
is not only

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we plotted all the real observation
points in the grid.

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So all the points that you see here are
the customers of either your training sets

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and then later on your test set,
the green points are, of course,

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the customers who bought the SUV,
you know, represented by one here.

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And the red points are,
of course, the customers who didn't buy

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the SUV represented by zero here.

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Okay, so all the points
are your observation points.

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Your customers.

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And then so the trick in order
to plot the prediction regions

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and therefore that prediction
boundary here separating the two regions

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is to apply to predict method

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onto each of these dense points
in the grid,

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so that all the dense points here,
you know, in this region

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were actually predicted to be zero,
meaning all the customers,

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you know, other customers inside this
region are predicted not to buy the SUV.

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And all the observation points
in this green

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region
are actually predicted to by the SUV.

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So you see how this works.
That's the trick.

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And then really
you don't have to understand

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all the techniques used to implement this,
because once again,

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you will probably never have to implement
that kind of code in your career.