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Hello. Welcome back to the course.

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Super excited to have you on board today.

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We've got a very interesting
and important tutorial.

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Assumptions of linear regression.

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So let's have a look.

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Here we've got a data set.

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With a linear regression applied.

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And this linear regression seems
to be serving its purpose really well.

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However if we look at the following
three data sets,

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we can see that
a linear regression is applied each time.

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And in fact it's exactly the same linear
regression as in the first case.

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However, those linear regressions
are not serving their purpose.

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In fact, they are misleading.

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So we shouldn't be using linear
regressions in those situations.

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These four data sets are called
the Anscombe Quartet,

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and they illustrate that you can't just
simply blindly apply linear regression.

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You have to make sure that your data set
is fit for using linear regression.

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And that's where assumptions of linear
regression come in.

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So let's have a look at them.

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There's going to be five
assumptions in total plus an extra check.

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The first assumption is linear.

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We want to make sure
that there is a linear relationship

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between our dependent variable
and each independent variable.

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And if you look at the chart

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here on the right, you'll see that
the linear regression is misleading.

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It is.

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There is actually no linear relationship
between the two variables.

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So we wouldn't use
this kind of model there.

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The second assumption is homoscedasticity.

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And even though

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it sounds like a complex term,
it actually simply means equal variance,

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meaning that you don't want to see
a cone type shape

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on your chart with an increasing cone
and decreasing cone,

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which would mean that variance
is dependent on the independent variable.

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So in this case we wouldn't
use a linear regression either.

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The third assumption
is multivariate normality

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or normality of error distribution.
If you look at the chart

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here on the right,
you can feel that something is off.

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The best way to intuitively
think about it is

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if you look along the line of the linear
regression,

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you want to see a normal distribution
of your data points.

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In the case on the right here,
we can see something different.

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And so again we wouldn't apply a linear
regression there.

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The fourth assumption
is independence of observations.

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And this includes the term
no autocorrelation.

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Sometimes you'll see this assumption
titled as no autocorrelation.

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And what that means is that we don't want

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to see any kind of pattern
in our data pattern in the data

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like we see here indicates
that our rows are not independent,

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that some rows are affecting other rows
and other rows, etc..

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A classic example of
this would be the stock market, where

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previous prices of future prices
which affect future prices and so on.

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So in this case, we wouldn't
apply a linear regression model.

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The fifth assumption is
lack of multicollinearity.

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Basically we want our independent
variables or predictors

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not to be correlated with each other
if they're not correlated

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then we can build a linear regression.

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If they are correlated

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then if we do proceed and build a linear
regression model, then the coefficient

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estimates that we get in
the model will become unreliable.

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And the sixth point is the outlier check.

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This is not an actual assumption,
but rather an extra check.

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That is important to keep in mind
when building linear regression models.

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If you look at the chart here
on the right, you can see that the outlier

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is significantly affecting the linear
regression line that we get.

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So something that we want to consider is

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should we remove the outliers
before building a linear regression.

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Or do we want to build a linear regression
with the outliers included?

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This will depend on your business
knowledge and knowledge of the data set.

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So there we go.

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Those are the assumptions of linear
regression.

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In this course
we're going to assume by default

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that they are correct
for all the data sets that we work with.

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However, when you're working
with your own data sets, it's important

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to do these checks to make sure you're
building a linear regression.

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When it is fit for the data set.

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And to finish off this tutorial,
I have a special bonus for you.

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If you enjoyed this explanation,
you can download the PDF

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version of this slide and keep it at home
printed out as a poster.

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Keep it somewhere handy

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for those times when you do need to check
assumptions of linear regression.

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If that's something
that you would like to have.

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Head on over to Super Data

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science.com/assumptions
and you can download your poster there.

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And I look forward to seeing you back here
next time.

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Until then, enjoy machine learning.