♪ [music] ♪
- [Thomas Stratmann] Hi!
In the upcoming series of videos,
we're going to give you a shiny new tool
to put into your Understanding Data toolbox:
linear regression.
Say you've got this theory.
You've witnessed how good-looking people
seem to get special perks.
You're wondering,
"Where else might we see this phenomenon?"
What about for professors?
Is it possible good-looking professors
might get special perks too?
Is it possible students treat them better
by showering them with better student evaluations?
If so, is the effect of looks
on evaluations really big or really small?
And say there is a new professor starting at a university.
What can we predict about his evaluation
simply by his looks?
Given that these evaluations can determine pay raises,
if this theory were true, we might see professors resort
to some surprising tactics to boost their scores.
Suppose you wanted to find out
if evaluations really improve with better looks.
How would you go about testing this hypothesis?
You could collect data.
First you would have students rate on a scale from 1 to 10
how good-looking a professor was,
which gives you an average beauty score.
Then you could retrieve the teacher's teaching evaluations
from twenty-five students.
Let's look at these two variables at the same time
by using a scatterplot.
We'll put beauty on the horizontal axis,
and teacher evaluations on the vertical axis.
For example, this dot represents Professor Peate,
- ["Star Wars"
who received a beauty score of 3
and an evaluation of 8.425.
This one way out here is Professor Helmchen.
- [Ben Stiller, "Zoolander"] Ridiculously good-looking!
- [Thomas] Who got a very high beauty score,
but not such a good evaluation.
Can you see a trend?
As we move from left to right on the horizontal axis,
from the ugly to the gorgeous,
we see a trend upwards in evaluation scores.
By the way, the data we're exploring in this series
is not made up -- it comes from a real study
done at the University of Texas.
If you're wondering, "pulchritude" is just the fancy academic way
of saying beauty.
With scatterplots it can sometimes be hard
to make out the exact relationship between two variables --
especially when the values bounce around quite a bit
as we go from left to right.
One way to cut through this bounciness
is to draw a straight line through the data cloud
in such a way that this line summarizes the data
as closely as possible.
The technical term for this is "linear regression."
Later on we'll talk about how this line is created,
but for now we can assume that the line fits the data
as closely as possible.
So, what can this line tell us?
First, we immediately see
if the line is sloping upward or downward.
In our data set we see the [fitted] line slopes upward.
It thus confirms what we have conjectured earlier
by just looking at the scatterplot.
The upward slope means that there is a positive association
between looks and evaluation scores.
In other words, on average,
better-looking professors are getting better evaluations.
For other data sets we might see a stronger positive association.
Or, you might see a negative association.
Or perhaps no association at all.
And our lines don't have to be straight.
They can curve to fit the data when necessary.
This line also gives us a way to predict outcomes.
We can simply take a beauty score and read off the line
what the predicted evaluation score would be.
So, back to our new professor.
We can precisely predict his evaluation score.
"But wait! Wait!" you might say.
"Can we trust this prediction?"
How well does this one beauty variable
really predict evaluations?
Linear regression gives us some useful measures
to answer those questions
which we'll cover in a future video.
We also have to be aware of other pitfalls
before we draw any definite conclusions.
You could imagine a scenario
where what is driving the association we see
is really a third variable that we have left out.
For example, the difficulty of the course
might be behind the positive association
between beauty ratings and evaluation scores.
Easy intro. courses get good evaluations.
Harder, more advanced courses get bad evaluations.
And younger professors might get assigned to intro. courses.
Then, if students judge younger professors more attractive,
you will find a positive association
between beauty ratings and evaluation scores.
But it's really the difficulty of the course,
the variable that we've left out, not beauty,
that is driving evaluation scores.
In that case, all the primping would be for naught --
a case of mistaken correlation for causation,
something we'll talk about further in a later video.
And what if there were other important variables
that affect both beauty ratings and evaluation scores?
You might want to add considerations like skill,
race, sex, and whether English is the teacher's native language
to isolate more cleanly the effect of beauty on evaluations.
When we get into multiple regression
we will be able to measure the impact of beauty
on teacher evaluations
while accounting for other variables
that might confound this association.
Next up, we'll get our hands dirty by playing with this data
to gain a better understanding of what this line can tell us.
- [Narrator] Congratulations!
You're one step closer to being a data ninja!
However, to master this
you'll need to strengthen your skills
with some practice questions.
Ready for your next mission? Click "Next Video."
Still here?
Move from understanding data to understanding your world
by checking out MRU's other popular economics videos.
♪ [music] ♪