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Now, the other very

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important thing to understand
is that these are two prediction regions

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separated by a straight line,
which is the straight line.

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Here.

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And the straight line is called
the prediction boundary,

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because it's the boundary
between the two prediction regions.

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And the fact that it's a straight
line is not random.

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It is for a particular reason.

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And that's the thing
very important to understand,

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because that's the essence
of logistic regression.

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If the prediction boundary
is a straight line here,

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that's because our logistic regression
classifier is a linear classifier.

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That means that here,
since we are in two dimensions, you know,

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because we have two independent variable
the age and the estimated salary.

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So we are in two dimensions.

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Then since the logistic regression
classifier is a linear classifier,

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then the prediction boundary separator
here can only be a straight line.

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If we were in three dimensions
then it would be

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a straight plan separating two spaces.

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But here in two dimensions
it's a straight line

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and it will always be a straight line.

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If your classifier is a linear classifier,
but you will see later

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that when we build non linear classifiers,

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then the prediction boundary separator
won't be a straight line anymore.

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I won't tell you more right now
and I will let you wait for the surprise.

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So here we can clearly see that our 
logistic regression classifier manages

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to catch most of the users who didn't buy
the SUV in the red region here,

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and most of the users who bought the SUV
in the green region here.

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So it actually did a pretty good job.

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However, it seems to have trouble
catching some green users here

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who in spite of their low salary,
but the luxury SUV,

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as well as those other green users here
who also bought the luxury SUV

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because as you can see,

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this green points here
and those here are in the red region,

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which is the region
where our classifier predicts

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that the users don't buy the SUV.

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And those incorrect predictions
are due specifically

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to the fact that our classifier
is a linear classifier.

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And because our users
are not linearly distributed,

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if they were linearly distributed,
then we will have all the green points

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here in the space
and all the red points here in this space.

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And then the linear classifier
with a straight line could

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perfectly separate all the red points
here, and all the green points here.

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But here we have some rebellious points
who are not in the wanted linear regions.

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And because our classifier has a linear
straight line separator,

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that's why it has trouble
catching those users here and those here.

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You can clearly see that
even if you try to rotate this straight

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line here, well, you will always have
some green points in the wrong category.

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For example, if we try to rotate here
this way, like putting it down, well

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okay, we will catch these green points
here and the right green region here.

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But since we rotated down
we will take more green users here

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because this will go up and more green
users here will be in the red region.

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So that's the best separator.

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The logistic regression
classifier could find.

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And it couldn't do better

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because it can only be a straight line
separating these two regions.

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Because to catch those users,
the green users here and the green users

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here in the red category
that is the green region are classified.

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We need to make some kind of a curve here
to, you know, classify

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correctly those green users here and here
and place them in the green region.

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And that would prevent our classroom from
making this incorrect predictions here

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because it is a straight line
with a curve.

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Here we would catch all the red users,
probably in the red region

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and all the green users
in the green region.

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So that would make an awesome classifier.

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And you will see

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how our nonlinear classifiers
will make a terrific job in doing this.

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I can't wait to show you this.

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Okay.

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And now eventually, the last thing
very important to understand is that

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this is the training set.

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This is a training set.

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So that means that

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our classifier learns how to classify
based on these informations here.

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So I would hold my breath
a few more seconds until I find out

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if our logistic regression classifier
can manage to make good predictions

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of new observations, that is, to classify
new users into the right regions,

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which, by the way, are fixed regions here,
because these are the regions

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generated by the learning experience
of our logistic regression classifier,

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and therefore won't change
if we look at some new observations.

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That is, new social network users,

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00:04:31,033 --> 00:04:34,033
and that's what we are about to find out
on the test set.

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So hold on.

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00:04:35,500 --> 00:04:37,500
So it's very simple.

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We're just going to copy
all this code section here.

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00:04:42,900 --> 00:04:44,100
Paste it here.

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00:04:44,100 --> 00:04:46,900
And I'm just going to change the training
set here.

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My test set.

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00:04:49,466 --> 00:04:52,833
Same here
I change training set by test set.

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And that's all.

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That's all because I structured the codes
in such a way

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00:04:56,566 --> 00:04:59,900
that we only need to change
the training set into the test set here.

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00:05:00,200 --> 00:05:03,200
To plot this graph on a specific set.

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00:05:03,366 --> 00:05:08,200
However, let's change the title here
because we want to specify

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00:05:08,200 --> 00:05:11,200
that it's the test set and it's ready.

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00:05:11,266 --> 00:05:14,333
So let's select this and execute.

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00:05:16,800 --> 00:05:19,800
Let's see what happens.

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00:05:19,966 --> 00:05:22,966
And here are the results of the test set.

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00:05:23,400 --> 00:05:24,433
So that's not too bad.

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00:05:24,433 --> 00:05:26,666
That's not too bad. Because as we can see

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00:05:26,666 --> 00:05:30,033
the major the majority of red points
are in the right region.

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That means the region predicted to be zero
and the majority of green points

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00:05:34,466 --> 00:05:35,966
are in the right region.

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00:05:37,166 --> 00:05:37,666
As for the

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training set, there are some observations
that were incorrectly predicted.

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That's normal.

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00:05:42,366 --> 00:05:46,166
That's because it's a linear classifier
and it cannot make a curve here.

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Catching all the right guys.

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00:05:49,333 --> 00:05:52,266
All right so that's it
for the interpretation of the graph.

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00:05:52,266 --> 00:05:55,566
I can't wait to show you
how we can make more powerful classifiers.

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And of course these
are going to be nonlinear classifiers.