Outliers

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- [Thomas] What is an outlier?

You probably already have
a good intuition of it.

It's that 6'10" kid in high school
who towers over his classmates.

It's that little guy
outeating people twice his size.

Outliers are those
that don't fit the pattern

we're used to seeing.

Let's go back to our data set.

If you remember,
we're examining the relationship

between professors' beauty scores
and their student evaluations.

We generally see
that better-looking teachers

get better evaluations.

Is there an outlier here?

This point.

It shows a professor
with an extremely high beauty score

but a very low evaluation score.

So, I guess in this case,
looks aren't everything.

A single outlier
can have a major effect.

We can see this in our data
by removing or adding points

and seeing the effect
on the regression line.

Let me show you.

If you right click
or control click,

you can remove a point
from our regression analysis.

Let's remove this outlier,
and see what happens.

The dotted line
is our old regression line,

and the solid one is our new one.

You can see it's gotten steeper.

That makes sense,
as we're removing an outlier

that is pulling the line down.

You can also see down below

that our slope value has changed
from 0.2 to 0.3.

So removing a single outlier
resulted in us finding

a much stronger relationship

between beauty
and evaluation scores.

If you remember, in our last video
we did an exercise

where we predicted the expected
change in evaluation score

when going from a 2 to a 7
in beauty score.

Our old slope was 0.2,

which meant a 1-point
predicted increase in evaluation.

With this new line,

we'd predict an increase
of 1.5 points in evaluation.

That's a 50% stronger effect,

and that's the power of an outlier.

That one really good-looking
but really bad teacher

is changing our model a lot.

The point is, regressions
can be sensitive to outliers.

If you want
to get your outlier back,

you can just click the undo button.

Additionally, we can add
data points to our regression

by just clicking
anywhere in the canvas.

You can see, again,
the line moves each time,

showing my new regression line
with a solid line

and the previous line
with a dotted line.

Now it's your turn.

I'd like you to try two things.

First, remove a point
so that the relationship weakens.

The line should get flatter,
so the slope should go down.

And, second, add some data points,
to make the relationship stronger.

So pause the video now,
and try it out.

- [Narrator] Find the answer

by clicking to see
the data in this video.

The link is also
in the video description below.

If you just want
to see the answer already,

hang tight.

Hopefully you've had some fun
adding and removing data points.

It's good to play with data
to build your intuition.

Let's cover the first question --

how to remove a point
to make the relationship weaker.

For example, remove this point.

You would have seen a flatter line

and our slope go down
from 0.2 to 0.14.

So how about to make
the relationship stronger?

Let's go back
to our original data set,

with a slope of 0.2.

If I add a point,
way up in the upper-right,

I can see my slope go up from 0.2.

I can also add one
to the lower-left,

and see another increase.

The more points I add
to these two regions,

the stronger the relationship gets.

So now that we've seen
the power of outliers,

your next question might be --
can I just remove the outlier?

it's important to remember
we're typically using a regression

to make a prediction
about the real world.

In the real world,

we see guys who are 130 pounds
eat 60 hot dogs.

So if you want to predict
hot dog eating based on weight,

removing an outlier without thought
can make your predictions worse.

However, in certain cases,

it might make sense
to remove an outlier.

What if you are trying to predict
the number of hot dogs

an average person would eat
at your upcoming barbeque?

Then, including Kobayashi would make
your prediction much worse.

In this case,
he's clearly an outlier,

and should be omitted
from the model.

You might have also noticed
something else changing

when we removed the outlier --
these funny numbers.

What do those mean?

That's what we turn to next.

- [Narrator] Congratulations!

You're one step closer
to being a data ninja!

If you want to master
linear regression,

Click to train up

on everything
from p-values to residuals,

and then prepare to unleash fury

on whatever poor data set
crosses your path.

Or, you can explore other skills

in our Understanding Data playlist.

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