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Hello and welcome back.

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Today we've got a very exciting tutorial.

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We're talking
about the logistic regression.

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The logistic regression is used to predict
a categorical

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dependent variable
from a number of independent variables.

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So the key difference
to a linear regression

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here is that we're not predicting
a continuous variable.

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We're predicting a categorical variable.

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For example you might be working
for an insurance company.

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And you want to predict
will somebody purchase

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the health insurance
that your company is offering.

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Yes or no.

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And it's a very simple yes or no.

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it's a categorical variable.

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And you might want to be predicting
this dependent variable,

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based on an, an independent variable
such as age.

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So depending on their age,
will they purchase,

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the health insurance plan
that your company is offering?

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So on the x axis we would have age.

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On the y axis we would have yes or no.

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Did they take up the offer or not?

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Let's say our x axis is somewhere between
18 years of age and 60 years of age.

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And our y axis
simply has a binary outcomes.

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Yes and no.

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So there's no in between this either
yes or no.

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So we're going to just add this horizontal
line for illustrative purposes.

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So what will our data set look like.

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Let's say we've got certain number
of observations in our data set.

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So we know people's age and we know,
when they were exposed to the offer,

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whether they purchased or didn't.

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So these people over here
didn't purchase, the health insurance.

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And these people over here

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did purchase the health insurance,
and that's our data set.

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So as you can see, it's very different.

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This plot looks very different
to what we were working with in the linear

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regression in tutorials.

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So we can't simply draw a linear
regression

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line as sloped a line
through these points.

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It makes no sense.

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So that's why the equation for logistic
regression is slightly different.

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Here it is.

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So, here on the left we've got,

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instead of y, we've got, a logarithm.

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And then on the right we've got,
the same, part as we saw before,

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the important value to us here is P,
and that is the probability

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that we'll be, working with just now.

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We'll see it in action.

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So let's look at the logistic regression
curve.

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The logistic regression curve
looks like this.

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And it's also called the sigmoid curve.

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And how does this work in action.

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Well let's say
we have two new observations.

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Let's say we've built this model
based on this data.

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we have a logistic regression.

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How will it apply to new observations.

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Well let's say
we have two new observations.

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Somebody of age 35 and somebody of age 45.

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what we do is
we will need to project these values

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onto our logistic regression,
find out where they fit there.

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And the logistic regression
will give us probabilities.

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So, this value 
everything here is between 0 and 1.

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So no is a zero.

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Yes is a one.

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And in between are the probabilities.

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So the logistic regression gives
us probabilities of somebody saying yes.

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So somebody's taking up that offer.

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So for the 35 year old it's a 42% chance

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that they will take up
the offer based on this model.

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So this is what the model is

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predicting is predicting a 42% chance
they will take up the offer.

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And for the 45 year old, there's an
81% chance they'll take up though.

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So we could stop there.

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That is the P.

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That is a probability
that we see in the equation on the left.

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that's hidden inside that logarithm.

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So we could stop there
and we could use these probabilities.

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Not in some use cases.

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That's
what the logistic regression is used for.

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We, we just deal with the probabilities
once we have them.

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But in most cases we want a binary
outcome, a yes or no outcome.

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And so for those situations,
we split our curve into two.

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I'll plug in to do anything above this
line, this middle line,

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anything above with a probability of 50%
or higher

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will be projected into a yes
into a binary one.

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And anything below the 50% line will be
projected into a no, a binary zero.

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How points would end up here?

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So based on this logistic regression,
we would make the conclusion

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that the 35 year old
would not purchase our insurance

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plan and the 45 year old
would purchase our insurance plan.

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And just like with linear regression,
you can have multiple independent

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variables.

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So for instance,
age, income, level of education,

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how big their families or whether
they have a family or they're single

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and many other types of variables
can be added depending on the, use case.

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And our equation
will look like this in this situation.

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So there you go.

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That's logistic regression in a nutshell.

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I look forward to seeing you next time.

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And until then enjoy machine learning.