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Hello my friends.

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All right.

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So let's implement quickly

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and efficiently the linear regression
model on the whole data set.

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First a quick reminder on
what is the linear regression model

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that we're about to build.

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We're simply
about to build this one right.

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Because we have only one feature
which is the position levels

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and the dependent variable,
which is of course the salary to predict.

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All right.

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So that's what we'll do first.

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And then we'll of course implement
the polynomial regression model with

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I will tell you how many powers
of that same position level feature.

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Okay.

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So let's do this
starting by creating a new code cell.

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All right.

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So I hope you did it yourself first
to make sure you refresh your skills.

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And so if that's the case of course
you stole it from the scikit learn library

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because that's the library
that contains this linear

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regression class which allows to build
a linear regression model.

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So scikit learn from which we're going

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to get access to the linear model
which contains this class.

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And from this linear model
we're going to import

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the linear regression
class as Google Collab.

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Guess it's perfectly perfect.
So that's the first step.

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Then we're going to create
an object of this class.

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So I know we used to call it regressor,
but this time

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since we're going to have two regressors,
you know we're going to have

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the linear regression regressor
and the polynomial regression regressor.

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Therefore this time I'm going to call it
Lin rake for linear regressor okay.

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So Lin rake will be created as an object
of this linear regression class.

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So I'm copying and pasting that here
adding some parenthesis.

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And remember we don't have to input
anything in these parentheses

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because there is not much to tune
in the linear regression model.

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Good.

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And finally now we have,
you know, the linear regression model.

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But it is not smart yet.

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It is not trained yet on this data set.

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You know, to understand
and learn the correlations

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between the position levels
and the salaries.

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So that's what we're going to do right now
by using this fit method,

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which is exactly a training method
that will train the model on these data.

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All right.

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So to do this
we're going to call our object first Lin

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Rag from which we're going to call the
fit method

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which remember has to take as input
the couple of matrix

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of features and dependent variable
vector of the training set.

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Right. That's what we did before.

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But remember here that we didn't split
the data set into a training set.

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And it just said
because we want to leverage

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the maximum data 
in order to train our model.

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And therefore this time we're going
to take the whole matrix of features X

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and the whole dependent variable
vector y'all. Right.

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So here we just input x and y
and there we go.

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We built the linear
regression model in a flashlight.

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So we're going to execute this.

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Here we go.

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And now we have not only our model
but also a trained model on this data set

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okay great.

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Now we're going to close this.

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And we're going to focus on

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the heart of the matter
which is the polynomial regression model.

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I'm going to teach you now how to build
the polynomial regression model.

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All right.
So we're going to create a new code cell.

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And now

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we're going to go back to this slide
to explain exactly what we're going to do.

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All right so as you understand what
we've just built so far is this model.

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We only have one feature

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the position levels and the dependent

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variable vector to predict
which are the salaries.

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Now what we're going to do
is we're going to create a multiple linear

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regression model.

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But instead of having different features
you know, X1, x2 and Zn,

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well these features will be x1,
x1, squared and x1 are the power of n.

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And we'll actually tune this parameter
a bit to try several powers.

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So not to confuse the polynomial.

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Linear regression is not a linear model,
because you will see that it can learn

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some nonlinear correlations, but
we call it polynomial linear regression

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because indeed there is this linear
combination of the squared and,

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you know, powered features
x1, x1, squared and x1 and the power of n.

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All right.

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And so the process of building
this model on Python

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will be first to create
a matrix of the powered features,

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you know a matrix of features
but not containing

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different features like X1, x2, an x n,
but a matrix of features containing x1

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as a first feature,
then x1 squared as a second feature,

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and then x1 to the power of
and as an end feature.

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So that will be our matrix of features,
and we will call it x poly.

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And then we will create a linear

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regressor object,
you know, from the linear regression class

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to integrate these powered features
of this matrix of features

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in this new linear regressor,
you see the idea.

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So it's a building process in two steps.

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We're going to first create
the matrix of features

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containing these features
at different powers.

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And then we'll integrate that
into a linear regression model.

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Because indeed this is a linear
combination of these powered features.

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All right perfect.

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So let's do this first step.

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The first step is to actually import
this tool

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that will allow us to create this
matrix of powered features.

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You know X1X1 squared
and x one are the power of n.

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And this class is called
polynomial features.

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So we're going to import it first

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which we can get from once again
of course the scikit learn library.

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There we go.

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But this time we're going to get access
to the pre-processing module

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which contains that polynomial features
class.

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This is a class because indeed
we're kind of preprocessing our X1 feature

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because we want to create out of x1 well
x1, x1 squared and x1 add the power of n.

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So we're kind of doing
preprocessing of the features.

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All right.

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So from this preprocessing module
we're going to import.

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Well that class put Li no more features.

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Perfect.