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♪ [music] ♪

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- [Thomas Stratmann] Hi!

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In the upcoming series of videos

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we're going to give you
a shiny new tool

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to put into your
Understanding Data toolbox:

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linear regression.

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Say you've got this theory.

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You've witnessed
how good-looking people

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seem to get special perks.

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You're wondering -- "Where else
might we see this phenomenon?"

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What about full professors?

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Is it possible
good-looking professors

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might get special perks too?

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Is it possible
students treat them better

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by showering them
with better student evaluations?

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If so, is the effect of looks

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on evaluation score
big or [inaudible]?

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And say there is a new professor
starting at the university.

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What can we predict
about his evaluation

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simply by his looks?

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Given that these evaluations
can determine pay raises,

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if this theory were true
we might see professors resort

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to some surprising tactics
to boost their scores.

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Suppose you wanted to find out

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if evaluations really improve
with better looks.

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How would you go about
testing this hypothesis?

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You could collect data.

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First you would have students rate
on a scale from 1 to 10

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how good looking a professor was,

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which gives you
an average beauty score.

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Then you could retrieve
the teacher's teaching evaluations

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from 25 students.

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Let's look at these two variables
at the same time

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by using a scatterplot.

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We'll put beauty
on the horizontal axis,

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and teacher evaluations
on the vertical axis.

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For example, this dot
represents Professor Peate,

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who received a beauty score of 3

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and an evaluation of 8.425.

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This one way out here
is Professor Helmchen.

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- [Professor Helmchen]
Ridiculously good-looking!

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- [Thomas] Who got
a very high beauty score,

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but not such a good evaluation.

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Can you see a trend?

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As we move from left to right
on the horizontal axis,

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from the ugly to the gorgeous,

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we see a trend upwards
in evaluation scores.

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By the way, the data
we're exploring in this series

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is not made up --
it comes from a real study

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done at the University of Texas.

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If you're wondering, "pulchritude"
is just the fancy academic way

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of saying beauty.

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With scatterplots
it can sometimes be hard

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to make out the exact relationship
between two variables --

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especially when the variables
bounce around quite a bit

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as we go from left to right.

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One way to cut through
this bounciness

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is to draw a straight line
through the data cloud

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in such a way that this line
summarizes the data

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as closely as possible.

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The technical term for this
is "linear regression."

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Later on we'll talk about
how this line is created,

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but for now we can assume
that the line fits the data

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as closely as possible.

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So, what can this line tell us?

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First, we immediately see

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if the line is sloping
upward or downward.

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In our data set we see
the [fitted] line slopes upward.

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It thus confirms what
we have conjectured earlier

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by just looking at the scatterplot.

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The upward slope means
that there is a positive association

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between looks
and evaluation scores.

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In other words, on average,

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better-looking professors
are getting better evaluations.

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For other data sets we might see
a stronger positive association.

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Or, you might see
a negative association.

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Or perhaps no association at all.

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And our lines
don't have to be straight.

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They can curve to fit the data
when necessary.

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This line also gives us
a way to predict outcomes.

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We can simply take a beauty score
and read off the line

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what the predicted
evaluation score would be.

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So, back to our new professor.

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- [Professor Lloyd] Look familiar?

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- [Thomas] We can precisely
predict his evaluation score.

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"But wait! Wait!" you might say.

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"Can we trust this prediction?"

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How well does
this one beauty variable

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really predict evaluations?

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Linear regression gives us
some useful measures

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to answer those questions

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which we'll cover
in a future video.

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We also have to be aware
of other pitfalls

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before we draw
any definite conclusions.

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You could imagine a scenario

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where what is driving
the association

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we see is really a third variable
that we have left out.

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For example,
the difficulty of the course

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might be behind
the positive association

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between beauty ratings
and evaluation scores.

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Easy intro. courses
get good evaluations.

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Harder, more advanced courses
get bad evaluations.

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And younger professors might
get assigned to intro. courses.

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Then, if students judge
younger professors more attractive,

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you will find
a positive association

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between beauty ratings
and evaluation scores.

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But it's really
the difficulty of the course.

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The variable that we've left out,
not beauty,

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that is driving evaluation scores.

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In that case, all the primping
would be for naught --

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a case of mistaken correlation
for causation,

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something we'll talk about further
in a later video.

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And what if there were
other important variables

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that affect both beauty ratings
and evaluation scores?

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You might want to add
considerations like skill,

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race, sex, and whether English
is the teacher's native language

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to isolate more cleanly the effect
of beauty on evaluations.

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When we get
into multiple regression

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we will be able to measure
the impact of beauty

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on teacher evaluations

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while accounting
for other variables

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that might confound
this association.

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Next up, we'll get our hands dirty
by playing with this data

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to gain a better understanding
of what this line can tell us.

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- [Narrator] Congratulations!

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

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However, to master this you'll need
to strengthen your skills

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with some practice questions.

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Ready for your next mission?
Click "Next Video."

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Still here?

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Move from understanding eata
to understanding your world

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by checking out MRU's
other popular economics videos.

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♪ [music] ♪