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Great.

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And now let's add the second component
which are the predictions.

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So I'm going to add a plus here
and add my second component here.

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So the second component is
as I just said the predictions.

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And we are going to add these predictions
component with the germline function.

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So exactly
like we did in simple linear regression.

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So geom line here serum underscore line
and then parenthesis of course.

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And again we are going to take
the a static function combined to a color.

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So I'm just going to copy all this right.

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And paste it in my germline function.

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All right.

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And now of course
we will change a few things.

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So first let's start with the simplest
the let's change the color.

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We're going to pick a blue color
for predictions.

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Here we go.

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And now what we need to change are
the coordinates of our prediction points.

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So the x coordinates of our prediction
points are still going

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to be the levels themselves.

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Because we're just predicting the salaries
of the ten levels

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that we have in our data set.

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So here we obviously need to take the only
levels that we have in our data set.

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So we keep here data set the level.

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But then for the y coordinates of course
something is going to change here

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because by taking data set

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our salary here, we are taking the real
salaries of our ten levels.

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That is the salaries that are
in the salary column of our data set.

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Here.

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So of course we need to remove this
and replace it by something else.

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And what is this
something else going to be.

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Well of course
it's going to be the predictions

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of the salaries of the ten levels
according to the linear regression model.

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And to get these predictions,
we are going to use of course the predict

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function.

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And so actually that's exactly the same
as in simple linear regression.

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In this predict function
we first need to specify the regressor.

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So the regressor is called Len rag
because you know

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we are plotting the linear
regression results.

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And our linear regression
model was called linear.

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That's our regressor.
So linear right here.

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And now the second argument
remember is new data.

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So new data here.

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And that's actually the data points
we want to make predictions on.

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So very simply that's our data set
because we want to get

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the predictions of the salaries
of the ten levels of our data set.

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So here we input indeed data set

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there.

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Perfect.

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So we're good because we already inputted
the blue color for our predictions.

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Great.

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And now let's complete this graph very
quickly by adding a title A plus here.

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And then you know we use the
G title function to add a title.

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Can you see how it's simple.

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It's starting to get really intuitive now.

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You know we are plotting
the real observation points with the jump

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point function, then the predictions
with the GM line function,

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and now a title with the target
title function.

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Well, everything will seem easier
and easier for you.

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So for the title
we're going to add as in Python truth

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or Bluff.

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You know, just to give a funny
name to our problem.

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And we're going to specify here that we
are plotting the linear regression result.

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So we will just specify
here linear regression.

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All right.

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So that's it for the title.

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And now let's add an x label
and a y label.

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So for the x label
we're going to add simply here

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x lab parenthesis then quotes.

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And then level.

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Because our x axis
will contain the levels.

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And then plus y lab parenthesis

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quotes and salary and done.

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The linear regression results
are ready to be plotted.

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So let's not wait anymore
and let's immediately have a look.

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So I'm going to select all this.

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I don't need to select this
because ggplot2 is already imported.

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And now let's press Command and Control
plus enter to execute.

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And here are the linear
regression results.

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So let's zoom on it and let's interpret.

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Great. Okay.

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00:04:07,800 --> 00:04:10,066
So what is the first thing
to understand here.

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Well the most important thing
to understand is definitely that

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we need to make the distinction
between the real observation points

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that are the red points here.

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Each point
correspond to one specific level

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and the real salary associated
to this level on the y axis here.

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And then we have our predictions
on this line that is that

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for each level
let's say for example the level five

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when we project this level
five here on this straight line

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here, this point is actually
our prediction point.

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And we can get the predicted salary
by projecting

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this point here on the y axis this way.

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00:04:47,400 --> 00:04:50,533
And so we get a little less than $250,000.

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Okay.
So that's the first thing to understand.

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The red points are the real observation
points.

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And the points on this blue
straight line are the prediction points.

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Okay.

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00:04:59,133 --> 00:05:01,100
Now the second
important thing to understand

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00:05:01,100 --> 00:05:04,733
is that our prediction result
is actually a straight line.

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00:05:04,966 --> 00:05:07,966
And the fact that it's a straight
line is due to a particular reason.

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It's that the linear regression
model is obviously a linear model.

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00:05:13,500 --> 00:05:18,000
Each time you build a linear model in two
dimensions, you'll get a straight line.

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00:05:18,300 --> 00:05:21,800
And I'm highlighting this because
the next model we are going to visualize

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the result is going to be
the polynomial regression model.

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And this model turns out
to be a non-linear regression model.

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And you will see that
it will not be a straight line anymore.