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Hello and welcome to this art tutorial.

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So in the previous tutorial,
we prepared our data correctly

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so that now we are ready
to fit our simple linear

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regression to our data set
without any issues.

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So we're going to do that right now.

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And as usual
we are going to use the simplest way,

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which is to take the LM function.

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So we're going to do that right now
we're going to call a new variable

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regressor.

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And that's going to be the simple linear

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regressor itself then equals.

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And then that's
where we use the LM function.

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So let's just type lm here.

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And then let's press F1 to see the info

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of this function
and especially the arguments.

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So let's see the first argument
we have to input is formula.

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So let's input it formula.

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And according to you
what is it going to be.

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Well this is going to be the dependent
variable

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expressed as a linear combination
of the independent variable.

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So here it's very simple.

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Since we only have one dependent variable
and one independent variable

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we just need to
type formula equals salary.

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Then I'll plus n.

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Here you go.

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And then we put the independent variable
which is years experience.

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So what does this notation means.

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That means that the salary is proportional
to years experience.

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Okay. So that's it for the first argument.

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That's the formula we need to input.

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And that's actually the simple linear
regression formula.

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And then we need to add a second argument

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which is let's see the data okay.

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And that's normal.

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That's because we have to specify to R
on which data

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we want to train our simple linear
regression model.

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And of course
this data is the training set.

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Because the training set is the set
on which you build your model.

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Okay. So that's it.

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Actually
I know there are some other arguments,

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but these are optional arguments
that we don't really need here.

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So we will just use this
two formula and data.

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Okay. So that's it.

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The regressor will be ready
once we select it and execute it.

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So let's do this right now.

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

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Here we go.

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Now the regressor is ready.

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As you can see it just appeared here.

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If you want to have some info about this
regressor then the best way to do it

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is to, you know,
go here in the console and type summary

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regressor because the name of our
regressor is regressor.

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Then type enter and then you have some
very good informations

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about your simple linear model
for example.

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Okay. So let's see.

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let's just put that up

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right.

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So first it tells you what the formula is
okay.

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So it's the salary being proportional
to the number of years of experience.

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And that the model is built
on the training set.

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Then you have some info
about the residuals.

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We won't be talking about this now.

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But the really important section
is this one coefficients.

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Because not only itself,

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the value of your coefficients
in the simple linear regression equation,

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but also it tells you the statistical
significance of your career efficiency.

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And here we observe three stars.

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Here.

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That means the years

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experience independent variable
is highly statistically significant

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because you can either have no star
or one star two stars or three stars.

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No star means
that there is no statistical significance,

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and three stars means that there is a high
statistical significance.

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So that's the first info.

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That's the first hint of
what is going to happen,

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because we already know by looking at this
that there will be a strong linear

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relationship between the salary
and the number of years of experience.

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And the other info here is the p value.

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Then the p value is another indicator
of the statistical significance,

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because the lower the p value is,

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the more significant
your independent variable is going to be.

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That is, the more impact, the more effect

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your independent variable is going to have
on the dependent variable.

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And usually a good threshold
for the p value is 5%, which means that

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when we are below 5%, the independent
variable is highly significant,

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and when we are over 5%,
that means that it's less significant.

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And here, as you can see, the p value
is 1.52 ten at the power of -14,

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which means that it's a very, very,
very small p value.

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So that means that this independent
variable

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years of experience
is highly statistically significant.

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And it has high impact and high effect
on the formula dependent variable.

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So that's very important information.

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Get the reflex to look at these by
you know typing summary regressor.

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Because this is really important
especially when you want to try out

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several potential independent variables.

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You need to look at their statistical
significance to choose them.

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And then
you have some informations of your model

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globally which will we'll be talking about
at the end of this part.

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Part one regression,

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when we'll be talking about ways
to evaluate your model when here.

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As you can see, you have the multiple
R-squared that we'll talk to you about.

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And the adjusted R-squared.

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If you have several models with several

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teams of independent variables,
then that's the adjusted R-squared.

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You must choose to choose the best model.

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All right.

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So that was just a parenthesis
to give you this very important trick

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to know in R and learn
how to evaluate your model already.

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So actually we are done

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fitting the simple linear regression
to our data set, our training set.

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And in the next tutorial
we are going to be predicting the test

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set results
to finally see how our simple linear

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regression behaves on a new set
on some new observations.

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Okay, so that's the end of this tutorial.

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I look forward
to seeing you in the next one.

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And until then, enjoy machine learning.