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Today we're talking about dummy variables.

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So basically the information that we have
is the profit

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of each, company or of each startup.

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Then the R&D spend, the admin
spend, the marketing spend.

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So those three are expenses
that the company incurred

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and then the state in which it operates,
either in New York or California.

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The challenge that we're faced with
is that the venture capitalist

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fund wants to see
if there's any correlations between profit

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and the amounts that have been spent on,

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different expenses, R&D,
admin and marketing, and also,

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whether on which in which state
the company operates.

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So is there a correlation between profit
and, all of these variables?

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And how would you go about
creating a model to understand

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how knowing R&D spend admin
and marketing and state to predict profit.

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And so therefore profit
is our dependent variable

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and the rest, the blue ones,
are all independent variables.

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And what we need to do
is build a linear regression.

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So let's go ahead and get started.

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As we would with multiple linear
regression.

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We would start by saying y which is profit
is equal to what.

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What is it equal to.

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Well, first of all, there's a constant.

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In this case it's b zero.

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And I've put it under the profit column
just because I needed to fit it somewhere.

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And then we would start adding on these, 
variables into our equation.

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So then we've got the b1 coefficient times
the X1 variable

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which is R&D spend in this case.

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And x1 is actually the amount, the dollar
amount that you see in the R&D column.

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Then you've got the admin.

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variable which is x2.

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It's got a coefficient of B2. Once again
admin.

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So in this case x2 is going to be the
dollar amount you see in the admin column.

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Then you've got the marketing spend

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x3 which will be the dollar amount
you see in the marketing column.

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And then you've got the state variable.

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And here when we get here
we're questioning

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what should we place in our equation
for the state column.

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Because we don't actually have a number,
we don't have a dollar value

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or any other type of number
to add into our equation.

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We can't just add a word
into our equation.

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And the thing here is that the state
is actually a categorical variable.

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So we talked about types
of variables before.

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And we understood that

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there's categorical variables
and there's numeric variables.

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Well in this case state
is a categorical variable.

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And therefore
we can't add it to our equation.

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We need to do something
about this situation

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and the approach that you need to take
when you face categorical variables

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in regression models is
you need to create dummy variables.

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Let's see how we we can do that.

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First you need to go through your column
and find all the different categories

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you have.
So in this case we have two categories.

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So for every single category that
you found you need to create a new column

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for New York.

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We're going to create
a column called New Yorker for California.

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We're going to create a column California.

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So we're kind of expanding our dataset and
adding some additional columns into it.

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And how do we populate the columns.

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So this is the fun part

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to populate these columns,
let's start with the New York column.

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You need to find all of your rows
where state actually says New York,

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and you need to.

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For those rows, you need to put a one in
the New York column and then in California

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and for all the rows that say, California,
basically for all the rows

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that don't say New York, whatever else
they say, you just put a zero.

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And then for California,
for the column California,

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you do the same thing
wherever a row says California.

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In the state column,
you place a one in the California column.

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And for any other values in the state

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column,
you place a zero in the California column.

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And so you end up with a data
set like this.

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And these two new columns
are called dummy variables.

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And building your
regression model from here is very simple.

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All you have to do
is use the New York column,

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and you're going to be using it
instead of states.

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You're not going to be
using state anymore.

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And basically you add a variable
which is B4 times D1

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and D1 in this case
is your dummy variable for New York.

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And you don't use the California
column either.

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So as you can see here, all of the
information in our data is preserved.

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If we just stick to the One New York
column, because you can tell right away

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if D1 is a one, then it's a company
that works in it operates in New York.

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If D1 is a zero, it's a company
that operates in California.

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So we didn't lose any information
by including only the New York column.

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And we will actually talk more
about why you should never include

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all of your dummy variable columns
in your regression model.

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We'll talk more about that
in the, next tutorial when we're talking

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about the dummy variable trap.

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But for now I would like to discuss
two things.

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So first of all,

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the New

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York column or all of the dummy variables
they work as switches.

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In this case.

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Let's look at the New York column,
which we're including in our regression.

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It works like a light switch.

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So if it's a one then you know that
this company is in New York

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if it's a zero.

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So off in this case,

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in the case of the picture, then
you know that the company doesn't work

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in New York options.

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So the dummy variables work
like light switches.

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And that's why they're ones and zeros and
they don't need any other values in them.

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And the second thing is that when you look
at this approach, it might seem biased.

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So we are including a variable
for New York.

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And there's a coefficient for new.

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So we basically have this benefit
of having

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a coefficient in our equation for New York
which is before.

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But for California there's no coefficient
because when D1 is zero,

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that whole last
part of the equation becomes zero.

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And there's no benefit of a coefficient
in our equation for California

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and might seem biased at first,
but in reality, that's not the case

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because the way regression models work
is that they will take by default

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that state or that variable, that dummy
variable that you have not included.

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It will become the default situation
for this regression model.

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So basically what that means
is that the coefficient for California

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is going to be included
in the constant in B0.

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And by default when d1 is equal to zero,

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this whole equation
will turn into an equation.

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You can think of it as it'll turn
into an equation for California.

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But then when d1 becomes one,
you're adding B4,

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which is once again
like this is a very basic explanation,

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but you're adding a coefficient,
which is the difference

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between New York and California.

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So so basically

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you'll altering from California
to New York by flipping this light switch.

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If it's on or off,
then kind of default state.

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And the whole equation
is working for California.

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If it's on on, then by adding that before
you're altering the equation

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from the default state
of California to New York.

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So that's a intuitive way
to think of dummy variables.

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So there's nothing wrong with the fact
that we're only including one.

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And once again, in the next tutorial,
we'll talk more about why

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it is a bad idea
to ever include both dummy variables.

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I'll look forward to seeing you
next time until then, happy analyzing.