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Hello and welcome to this art tutorial.

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So today in this tutorial,

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we are ready to fit multiple linear
regression to the training set.

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So as for simple linear regression,
the first thing that we're going to do

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is to introduce
the multiple linear regressor.

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And we're going to call it regressor.

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And then as for simple linear regression
we're going to use the lm function

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here lm.

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And in parentheses
we're going to input the parameters okay.

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So let's have a look at the LM
function here by pressing F1.

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Here we go. Fitting linear models.

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Let's look at our arguments.

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So that's the same as for simple linear
regression.

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Actually the first argument is formula.

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But this time you're going to see how
we will need to change the formula syntax.

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And then the second compulsory argument
to import is the data.

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And of course
it's going to be the training set.

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So let's first input the formula.

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So formula here.

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So remember in simple linear regression

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we wrote the formula salary proportional
to years experience.

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And here it's almost going to be the same.

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But the difference is that we have several
independent variables.

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We have four independent variables.

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In simple linear regression
the dependent variable

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was proportional
to the only independent variable.

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Well here it's going to be the same.

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The profit is going to be proportional
to these independent variables.

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Only the correct way to say
it is not proportional, but is the profit

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is going to be a linear combination
of the independent variables,

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and formula equals profit

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and n.

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And here the idea is to add
all the independent variables

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separated with a plus sign.

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So let's look at them.

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It's r d spend

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I'm using the dot here
because in the data set

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we have some spaces
and I'll replace them by dots.

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So here it's dot then.

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Plus and then the other variable
which is administration

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plus marketing spend

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spend plus state.

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And that's all.

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So that's how you express the profit

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as a linear combination
of all these independent variables.

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However there is a trick to write
this formula in a much more efficient way.

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It's instead of writing
all the independent variables here,

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we can simply write a dot.

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That's what we can simply write.

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And that's the exact same equation.

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R understands
that you want to express the profit

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as a linear combination
of all the independent variables.

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So the dot here just means
all the independent variables okay.

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So that's for the first argument.
Formula equals

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profit as a linear combination
of all the independent variables.

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And the second argument is data.

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And as we said it is
of course the training set

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because we want to train
our multiple linear regression model

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on the training set and then test
the performance on the test set later.

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All right.

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So that's it for building
our multiple linear regression regressor.

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So we're going to select this and execute.

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Here we go.

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And now now
there is something very important to do.

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And this is something very practical
very useful in R it's that we are going to

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look at the informations of our regressor
that we just built here.

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And to do this it's really, really simple.

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We just need to it's actually
like simple linear regression only here.

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This time
it's going to be more interesting

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because we will have several
independent variables,

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and some of them will have a stronger
effect on the dependent variable.

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So we'll see. It's
going to be more interesting.

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And so like in simple linear regression
we're going to write a summary

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of our regressor.

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All right.

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And just press enter.

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And that's
it I'm just going to move that up.

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And here we have
all the info of our regressor okay.

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So here the first thing is just a reminder
of what the formula is.

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So the profit is expressed
as a linear combination

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of all the independent variables.

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And our regressor is trained
on the training set.

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Okay. Perfect residuals.

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We will be talking about that
at the end of this part.

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So let's not focus on that right now.

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However that's the important part.

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The coefficients here.

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That's what we need to focus on right now.

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Because as you can see it gives some info

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for each of your independent variable.

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Or by the way state two and state three.

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Here are the dummy variables.

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And that's because, you know,
I told you that the library

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takes care of everything for you.

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Not only it created
the dummy variables are

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knew that it had to create dummy variables
for the state variable, and we helped R

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to understand that because we encoded
the state variable as factors.

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So or did all the job for you
because not only he created the dummy

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variables for the state variable,
but also R didn't fall into the dummy

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variable try because as you can see, it
automatically removed

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one of the dummy variable
to avoid some redundant dependency.

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So that's perfect.

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That's the beauty of, our libraries
as well as Python libraries and Python.

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I know we specified a new section
to remove the dummy variable,

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but that was just to remind you
about the trap.

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We don't need to do it.

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R and Python take care of that for you.