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All right.

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So good.

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Now we're going to do the same.
For the test result.

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So I'm just going to copy everything here
and paste that in a new.

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Code cell right here.

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And so now we're going to.

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Do the right.

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Replacements in this code
in order to visualize this I'm not the.

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Training set results
but the test set results.

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And so obviously.

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The first thing we need to replace
here are the.

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Coordinates.

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Of the real observations.

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Because these are the coordinates of,

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you know, the employees
in the training set.

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And we want the coordinates
of the employees. Of the test set.

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Therefore here we have to replace
obviously X trained by X test.

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And then Y train by. Y test.

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Okay.

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So these are for the real.

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Observations
with the numbers. Of years of.

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Experience and the.

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Real salaries of the test set.

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And now.

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According to you, do we have to replace.

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Something here in PLT.

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Plot x. Train.

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Regressor dot predict x train
according to you, do we have to replace.

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X train by x. Test.

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And the same x trained by x. Test.

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Well you know that's
kind of a trick question because remember.

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That the.

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Regression line that.

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We get is actually resulting.

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From a unique equation.

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And therefore the predicted
salaries of the test set will be.

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On the same regression line as.

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The predicted salaries of.
The training set.

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And that's.

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Why here
we actually don't have to replace X.

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Train by.

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Test. Here and here. Okay.

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You would actually get the.

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Exact same regression line.

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Whether you plot the.

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Coordinates. Of X train and the predicted.

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Salaries of training set.

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Or X. Test and the predicted.

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Salaries of the test set, you can check.

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But that's because the.

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Regression line in a simple linear
regression model.

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Results. From a unique equation.

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And we therefore end up
with the same regression line.

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Okay. So no need to replace anything here.

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And finally we.

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Will just replace.

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Your training set. By test set.

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And there you go.

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Now we're ready to visualize.

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The training set results
and the. Test set results.

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So let's first. Run the cells we haven't.

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Executed before.

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So remember we.

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Executed up to. The training.

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So now we have to execute this one
to indeed.

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Get the vector y pred
of the predicted salaries of the test set.

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So there we. Go. We now have y pred.

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And so now we're going to.

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First execute this
to visualize the training set results.

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And we're going to obtain.

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Now nice 2D plot with. Indeed.

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The real salaries.
In these red points here.

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And of course.

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Our beautiful. Regression line
containing the.

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Predicted salaries.

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And we clearly see that this. Regression
line was.

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Calculated so that.

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It comes as.

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Close as possible to the real salaries.

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And of course, for each of the years of.

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Experience here, in order to.

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00:02:43,966 --> 00:02:47,033
Get the predicted salary,
you have to project the.

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Year of experience.

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To this blue.

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00:02:49,566 --> 00:02:51,666
Regression line. So, for example.

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The predicted salary.

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Corresponding
to. Eight years. Of experience.

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Is about.

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You know, 100,000. Dollars per year. Okay.

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So that's how it works.
And so we can clearly.

91
00:03:01,766 --> 00:03:06,800
See that our predicted salaries
are very close to the real salaries.

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You know, for most of them.

93
00:03:08,600 --> 00:03:10,300
But that's on the training set.

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00:03:10,300 --> 00:03:12,700
Remember that's important
because our model was.

95
00:03:12,700 --> 00:03:15,466
Actually. Trained.
With these observations.

96
00:03:15,466 --> 00:03:18,366
You know. With these years. Of experience
and. Salaries.

97
00:03:18,366 --> 00:03:19,133
Now what we would.

98
00:03:19,133 --> 00:03:21,233
Like to observe is if we have.

99
00:03:21,233 --> 00:03:23,966
The same results,
you know, the same closeness.

100
00:03:23,966 --> 00:03:25,800
Of the. Regression line to the real.

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Salaries in the test set with.

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Which the model wasn't trained.

103
00:03:30,133 --> 00:03:33,133
You know, we want to evaluate it
on new observations.

104
00:03:33,166 --> 00:03:36,433
And that's exactly what this new graphic
will tell us.

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00:03:36,600 --> 00:03:38,566
Because now we were about. To plot.

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00:03:38,566 --> 00:03:39,866
This time, the real.

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00:03:39,866 --> 00:03:42,166
Salaries of the test. Set and the.

108
00:03:42,166 --> 00:03:44,633
Predicted salaries at. The same. Test set.

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So there we. Go.
Let's run this cell and let's.

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See if we're still close to the real
salaries.

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Even for new observations.

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And yes.

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Absolutely are predicted salaries,
which are of.

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00:03:56,200 --> 00:03:59,733
Course on the blue line
once again are very close indeed to the.

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00:03:59,733 --> 00:04:01,166
Real salaries.

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So our model or a simple linear regression
model.

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Was able to.

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Do a wonderful. Job at predicting.

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New observations.

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00:04:09,300 --> 00:04:10,533
So congratulations.

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00:04:10,533 --> 00:04:11,533
That's very exciting.

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00:04:11,533 --> 00:04:12,966
You built. A very successful.

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First machine learning model.

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00:04:14,700 --> 00:04:16,800
However, just remember. That.

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The reason why we. Get such a good.

126
00:04:19,300 --> 00:04:20,600
Regression line here.

127
00:04:20,600 --> 00:04:22,666
Is simply because there was a linear.

128
00:04:22,666 --> 00:04:25,633
Relationship in the data
set between the features

129
00:04:25,633 --> 00:04:27,733
and the dependent variable of.
The data. Set.

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00:04:27,733 --> 00:04:29,500
In other words. We had a perfectly.

131
00:04:29,500 --> 00:04:30,933
Linear data. Set.

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00:04:30,933 --> 00:04:32,366
In other. Words, we had a data set.

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00:04:32,366 --> 00:04:34,033
With linear correlations.

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00:04:34,033 --> 00:04:36,266
And what I want to make sure
you understand is that.

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These beautiful results.

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00:04:37,800 --> 00:04:39,300
Won't happen for any.

137
00:04:39,300 --> 00:04:41,400
Data set,
because of course, you'll get to.

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00:04:41,400 --> 00:04:44,400
Work on data
sets with non-linear relationships.

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00:04:44,600 --> 00:04:47,600
And for these data sets,
you will need a non-linear model.

140
00:04:47,733 --> 00:04:50,000
And that's exactly why. In this part.

141
00:04:50,000 --> 00:04:51,500
Two. Regression, we.

142
00:04:51,500 --> 00:04:54,600
Will also study. Some nonlinear models.

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00:04:54,600 --> 00:04:55,533
Which you will see will be.

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00:04:55,533 --> 00:04:56,900
Polynomial regression or.

145
00:04:56,900 --> 00:04:59,166
SVR, which will allow you to.

146
00:04:59,166 --> 00:05:00,066
Get amazing.

147
00:05:00,066 --> 00:05:01,633
Results for data.

148
00:05:01,633 --> 00:05:03,633
Sets having non-linear. Relationships.

149
00:05:03,633 --> 00:05:06,800
But for this data set,
we clearly had linear relationships.

150
00:05:06,800 --> 00:05:07,166
And that's.

151
00:05:07,166 --> 00:05:09,133
Why, Linear regression model.

152
00:05:09,133 --> 00:05:10,233
Was perfectly. Fine.

153
00:05:10,233 --> 00:05:12,800
But I just. Wanted to highlight this okay.

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00:05:12,800 --> 00:05:14,666
So congratulations once again, I.

155
00:05:14,666 --> 00:05:17,566
Hope you're very happy
and excited to have built your very.

156
00:05:17,566 --> 00:05:19,033
First machine learning model.

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00:05:19,033 --> 00:05:21,300
Now we're going to increase.
The difficulty a bit.

158
00:05:21,300 --> 00:05:25,266
Because in the next section
we will build a multiple linear regression

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00:05:25,266 --> 00:05:29,033
model, meaning that
instead of having one feature,

160
00:05:29,033 --> 00:05:31,166
you know only one independent variable.

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00:05:31,166 --> 00:05:33,700
We will have several of them.
And that's. Exactly the.

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00:05:33,700 --> 00:05:37,333
Difference between simple linear
regression and multiple linear regression.

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00:05:37,566 --> 00:05:40,366
Simple linear regression is
when you have only one feature,

164
00:05:40,366 --> 00:05:43,466
and multiple linear regression
is when you have several features.

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00:05:43,833 --> 00:05:44,700
So take a.

166
00:05:44,700 --> 00:05:46,700
Good break now, and as soon as you're.

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00:05:46,700 --> 00:05:49,500
Back with your energy.
Let's implement. Our.

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00:05:49,500 --> 00:05:52,433
Second machine learning model
in the next practical.

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00:05:52,433 --> 00:05:54,400
Activity after.

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00:05:54,400 --> 00:05:55,633
Intuition lecture.

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00:05:55,633 --> 00:05:57,466
And until then, enjoy machine learning.