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All right.

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So what we're going to do now
is we're going

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to get that whole code,
you know, from the original file.

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We're going to paste it
inside or new implementation.

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There we go.

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And we're going to do the same
for the to set.

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And then I will actually try

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not to show you the test it now
but let's get the code.

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Let's paste that below in a new code cell.

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And now let's enjoy the results.

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So what we're going to do is first execute
the cell.

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It's going to take a little while actually
because you know the step is oh point

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25 meaning we will get a very very dense
grid as I've just explained.

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And therefore, you know, the predict

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method is applied
on each of these dense points of the grid.

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And that's why they're actually a lot,
lot, lot of predictions to compute.

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And that's why it's taking a little time.

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But there you go. It's coming.

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Here we go.

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So not that long. That's good.

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We just got the results
of the training set.

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Let's also plot
now the results of the test set.

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And then I will make my comments
on the results.

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All right.

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So we can just let it run

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and start by observing and interpreting
the results of the training set.

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All right.

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So just to recap you have to understand
four things in this plot.

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Is that all the points that you see here,
whether they're red or green,

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are the real customers, and they're real
results in the training set.

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The green points correspond,
of course, to the customers

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who bought the previous SUVs,
and the red points correspond,

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of course, to the customers
who didn't buy any previous SUV.

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And then the other two things to
understand is that those colored regions

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here, you know, this red region and the
green region are the prediction regions.

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So this region is the region
where our model predicts

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that the customer didn't buy the SUV.

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And this region is the region
where our largest regression

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model predicts that the customers
but the previous SUV.

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And so in order to figure out
where the correct predictions are

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and the incorrect predictions are, well,
the correct predictions are where we have

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some observation points
with the same color

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as the prediction region,
and the incorrect predictions are

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where we have some observation points
with a color that is different

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than the prediction region.

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So for example, this customer here
who in reality

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but the SUV, you know,
corresponding to one here

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is actually an incorrect prediction
because it falls into the wrong region.

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The red region, and vice versa.

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This customer here, who in reality
didn't buy the SUV because it corresponds

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to zero, well, it's the wrong prediction
because it falls into the green region

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where customers are predicted
to buy the SUV.

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And then finally,

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what's the most interesting in all
this is the prediction boundary.

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As you understood,
the prediction boundary is

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the boundary
between those two prediction regions.

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You know, the green prediction region
and the red prediction region.

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It is where your classifier separates

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basically the two classes
the class one and the class zero.

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And now you have to understand
something very, very important.

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It is the fact, you know,
it is the observation that the prediction

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curve of the logistic regression
model is actually

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a straight line for one specific reason.

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It is because the logistic regression
model is a linear classifier.

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For any linear classifier,
the prediction boundary

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or the prediction
curve will always be a straight line.

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You know, in two dimensions.

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In three dimensions
it will be a straight plan.

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Okay, so that's
what we get for linear classifier.