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Hello my friends.

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Welcome to this new practical activity
on polynomial regression.

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This time we're going to learn
how to build together

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a nonlinear regression model,
which will allow us to tackle a problem

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with a non-linear data set, meaning a data
set with nonlinear relationships

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on which therefore a multiple linear
regression model would not be relevant.

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Now we're all going to go into part
two regression,

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and this time we're going to go to section
six polynomial regression to learn

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how to build indeed this nonlinear
regression model.

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All right.

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And as usual we're going to start
with Python inside which you will find two

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files polynomial regression ipynb which is
of course your Python implementation

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which you can open either in Google Colab
or Jupyter Notebook.

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And the data set called position salaries.

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All right.

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So as usual we going to start
by describing the data set.

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Once again I'd like to remind that
this is a simple data set.

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But no worries.

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The further we progress in this course,
the more we will work with real world

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and complex data sets.

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You will see at the end we will work with
data sets with many more observations

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and more complexities.

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So what is this data set about?

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Well let's imagine the following scenario.

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Let's imagine
that we are actually an HR department

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and that we want to hire someone.

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And we actually found someone
that seems to be a great fit for the job.

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So we would like to offer this person
a position in our company.

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And so this person says yes,
but at the end of the interview process

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comes the inevitable question
what is your salary expectation?

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And let's say that this person is, you
know, very well advanced in its career,

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and therefore that person
is asking for $160,000 per year.

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And then also as HR negotiators,

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we ask this person,
why are you expecting such a high salary?

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And this person replies,

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well, that's because that's
what I earned in my previous company.

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That was my salary.

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In my previous company,
I earned $160,000 per year.

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So I'm expecting at least $160,000
per year in your company.

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Is that the truth, or is that a bluff?

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Well, that's
exactly what we're going to figure out.

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Thanks to our polynomial regression model.

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We're going to build
a polynomial regression model

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to predict the previous salary
of this candidate.

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So how are we going to do this?

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Well, of course in order to make such
a prediction we need data.

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And that's exactly the data
we collected here.

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So what is this data
and how did we collect it.

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This data is actually the different
salaries of the previous company

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for the different positions
from business analyst to CEO.

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And now how did we collect such data.

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Well you know there are many websites
online which actually display

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the different salaries
of the different positions in companies.

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I can give you an example like Glassdoor.

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Well, let's say that we did this
and that's how we collected all this

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data containing all the salaries
for the different positions

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of this previous company
for which this person worked.

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Okay.

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So we have this data
and now we need to know obviously

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which position this person
had within this previous company.

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Well that's easy.

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Let's say we went to LinkedIn and
we checked out the profile of this person.

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And we actually saw that this person
was actually a region manager.

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Okay.

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However, on the LinkedIn
we also see something else.

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It turns out that this person actually
has been a region manager

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for quite a while,
like let's say two years and therefore,

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you know, the salary of this person
should not exactly be $150,000,

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as we can see on this data set,
but instead it should be

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somewhere between 100 and $50,000,
the salary of position

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number six and $200,000
the salary of position number seven.

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So in order to extrapolate,
we're going to suppose that

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this person has a position in between 6
and 7.

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And we'll consider this position
to be 6.5,

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so that then
we can actually deploy our model,

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you know, after training it
of course, on the position level 6.5,

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so that we can get the predicted salary
of such a position level.

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And we will compare this predicted salary
to the salary expected by this person,

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to see if indeed there is truth or bluff.

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All right.

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Are you ready?

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Let's do this.

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Let's build
our polynomial regression model.