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And this little

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something that we're going to add
is actually the polynomial features.

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The polynomial features are actually
some additional independent variables

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that are going to be the level squared,
the level cubed level

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to the fourth level
to the fifth up to any degree you want.

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These are these additional independent
variables.

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There are going to compose
our new matrix of features in some way,

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which will actually be the matrix

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on which we will apply a multiple linear
regression model,

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which will make the whole model
a polynomial regression model.

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So in short, a polynomial regression
model is a multiple linear regression

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model that is composed of one independent
variable and additional independent

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variables that are the polynomial terms
of this first independent variable.

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Okay, so now that we get this idea,
you'll perfectly understand

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what we're about to do right now when
building our polynomial regression model.

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Because what we are going to do
is to build this polynomial terms.

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And to that extent, what we're
simply going to do is to add specifically

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a new column here in this data set,
which will be the level squared.

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So we're going to call
this new independent variable level two.

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And let's add this new column right now.

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So to add a column in a data frame
we need to take our data frame.

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So its data set.

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Here it is.

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And then we need to add
a dollar sign here.

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And then we can add any name here which
will create a new column of this name.

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And add it into our data set.

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So we're going to call this column
level two

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because we're taking the level
squared of our ten levels.

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Then we add equals.

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And then we actually need
to give the formula

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of the values in this level
two column of our data set.

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And this formula is therefore the levels
in our data set at the power of two.

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So very simply we're going to take

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all the levels of our data
set by taking our data set.

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And same adding this dollar here

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to take the level column, which is here,
I just have to press enter.

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So by doing this I'm
taking the level column.

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That is all the values of the level column
in our data set.

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And now I'm going to take the square
of all these levels in our data set.

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And so to do this very simply
I just add hat.

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And two that's it
that we'll just create a new column

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which will contain the squares
of our ten levels in our data set.

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So let's see right now
my data set contains only two columns

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level and salary. And if I execute this

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here we go.

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Now let's have a look at the data set.

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As you can see I now have three columns
level salary and level two.

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And as you can
notice the values in the level two column

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are the squares of the values
in the level column.

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Okay.

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And now we can build
our polynomial regression model.

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Because now this dot here
not only contains the level column

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but also the level two column.

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So this will build a multiple linear
regression model

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where the independent variables
are the original independent variable

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and the polynomial term
of this first independent variable.

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And if you want to build
a polynomial regression

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model with a higher degree, well,
you will need to do the same here.

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You know,
we can copy this line and paste it here.

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And just add a level
three column that will contain the cubes

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of the levels in the original independent
variable level of our data set.

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And as you can see, it'll be very easy.

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I just need to execute this line.

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And this will add a level
three column in our data set.

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And so now this little dot here will be

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the original independent variable level,
the square values of our levels

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in level two and the cube values
of our levels in the column level three.

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You can add as many powers of levels
as you want, but maybe we will stop here.

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We will see what is the best
polynomial regression for our model.

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And so we will see what
we'll get with this one.

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And now let's actually build
the polynomial regression model.

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If we select this and execute press
Command and Control plus enter to execute

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and run our polynomial regression
model is created.

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Awesome.

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So we're going to have a look.

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Let's type
summary in the console poly rag.

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And let's press enter.

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And let's see where we get okay.

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So now what we can see is that these level
two and level three polynomial terms

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that we created are actually
statistically significant variables.

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But actually this table here does not show

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the real deal of the polynomial regression
model for our problem.

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You will be much more convinced

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in the next tutorial, we will be
visualizing the graphic results,

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and you will perfectly understand
why our polynomial regression,

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which is a non-linear model, will make a
much better job at predicting what we want

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compared to this linear regression model,
because it's a linear model.

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So we'll check that in the next tutorial.

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And until then, enjoy machine learning.