0:00:00.107,0:00:03.926
♪ [music] ♪

0:00:20.880,0:00:22.077
- [Thomas Stratmann] Hi!

0:00:22.077,0:00:24.268
In the upcoming series of videos,

0:00:24.268,0:00:26.858
we're going to give you[br]a shiny new tool

0:00:26.858,0:00:30.414
to put into your[br]Understanding Data toolbox:

0:00:30.414,0:00:31.981
linear regression.

0:00:32.885,0:00:34.668
Say you've got this theory.

0:00:34.668,0:00:37.249
You've witnessed[br]how good-looking people

0:00:37.249,0:00:39.067
seem to get special perks.

0:00:39.642,0:00:40.878
You're wondering,

0:00:40.878,0:00:43.798
"Where else might we see[br]this phenomenon?"

0:00:44.132,0:00:45.637
What about for professors?

0:00:45.637,0:00:48.259
Is it possible[br]good-looking professors

0:00:48.259,0:00:50.010
might get special perks too?

0:00:50.350,0:00:53.899
Is it possible[br]students treat them better

0:00:53.899,0:00:57.209
by showering them[br]with better student evaluations?

0:00:57.866,0:01:00.467
If so, is the effect of looks

0:01:00.467,0:01:03.573
on evaluations really big [br]or really small?

0:01:04.349,0:01:08.263
And say there is a new professor[br]starting at a university.

0:01:08.619,0:01:11.810
What can we predict[br]about his evaluation

0:01:11.810,0:01:13.371
simply by his looks?

0:01:13.940,0:01:17.216
Given that these evaluations[br]can determine pay raises,

0:01:17.671,0:01:21.709
if this theory were true,[br]we might see professors resort

0:01:21.709,0:01:24.980
to some surprising tactics[br]to boost their scores.

0:01:25.471,0:01:27.461
Suppose you wanted to find out

0:01:27.461,0:01:30.801
if evaluations really improve[br]with better looks.

0:01:31.441,0:01:34.450
How would you go about[br]testing this hypothesis?

0:01:34.956,0:01:36.552
You could collect data.

0:01:36.761,0:01:40.025
First you would have students rate[br]on a scale from 1 to 10

0:01:40.025,0:01:42.076
how good-looking a professor was,

0:01:42.076,0:01:44.807
which gives you[br]an average beauty score.

0:01:45.229,0:01:48.552
Then you could retrieve[br]the teacher's teaching evaluations

0:01:48.552,0:01:50.421
from twenty-five students.

0:01:50.421,0:01:53.273
Let's look at these two variables[br]at the same time

0:01:53.273,0:01:54.738
by using a scatterplot.

0:01:54.981,0:01:57.419
We'll put beauty[br]on the horizontal axis,

0:01:57.852,0:02:00.589
and teacher evaluations[br]on the vertical axis.

0:02:01.463,0:02:03.173
For example, this dot[br]represents Professor Peate,

0:02:03.173,0:02:06.173
- ["Star Wars"

0:02:06.173,0:02:08.811
who received a beauty score of 3

0:02:08.811,0:02:11.866
and an evaluation of 8.425.

0:02:12.084,0:02:14.958
This one way out here[br]is Professor Helmchen.

0:02:14.958,0:02:16.797
- [Ben Stiller, "Zoolander"][br]Ridiculously good-looking!

0:02:16.797,0:02:18.721
- [Thomas] Who got[br]a very high beauty score,

0:02:18.721,0:02:20.872
but not such a good evaluation.

0:02:21.101,0:02:22.283
Can you see a trend?

0:02:22.283,0:02:25.533
As we move from left to right[br]on the horizontal axis,

0:02:25.533,0:02:27.963
from the ugly to the gorgeous,

0:02:27.963,0:02:31.186
we see a trend upwards[br]in evaluation scores.

0:02:31.870,0:02:35.174
By the way, the data[br]we're exploring in this series

0:02:35.174,0:02:38.923
is not made up --[br]it comes from a real study

0:02:38.923,0:02:40.897
done at the University of Texas.

0:02:41.337,0:02:46.023
If you're wondering, "pulchritude"[br]is just the fancy academic way

0:02:46.023,0:02:47.880
of saying beauty.

0:02:48.405,0:02:51.474
With scatterplots[br]it can sometimes be hard

0:02:51.474,0:02:55.594
to make out the exact relationship[br]between two variables --

0:02:55.594,0:02:59.104
especially when the values[br]bounce around quite a bit

0:02:59.104,0:03:01.318
as we go from left to right.

0:03:02.000,0:03:04.908
One way to cut through[br]this bounciness

0:03:04.908,0:03:08.144
is to draw a straight line[br]through the data cloud

0:03:08.144,0:03:10.775
in such a way that this line[br]summarizes the data

0:03:10.775,0:03:12.613
as closely as possible.

0:03:13.295,0:03:17.181
The technical term for this[br]is "linear regression."

0:03:17.669,0:03:20.888
Later on we'll talk about[br]how this line is created,

0:03:20.888,0:03:24.278
but for now we can assume[br]that the line fits the data

0:03:24.278,0:03:26.456
as closely as possible.

0:03:27.087,0:03:29.536
So, what can this line tell us?

0:03:30.067,0:03:32.596
First, we immediately see

0:03:32.596,0:03:35.358
if the line is sloping[br]upward or downward.

0:03:36.107,0:03:39.827
In our data set we see[br]the [fitted] line slopes upward.

0:03:40.794,0:03:43.807
It thus confirms what[br]we have conjectured earlier

0:03:43.807,0:03:45.587
by just looking at the scatterplot.

0:03:46.070,0:03:50.237
The upward slope means[br]that there is a positive association

0:03:50.237,0:03:53.026
between looks[br]and evaluation scores.

0:03:53.544,0:03:55.907
In other words, on average,

0:03:55.907,0:03:59.469
better-looking professors[br]are getting better evaluations.

0:03:59.768,0:04:03.939
For other data sets we might see[br]a stronger positive association.

0:04:04.377,0:04:07.420
Or, you might see[br]a negative association.

0:04:07.857,0:04:10.764
Or perhaps no association at all.

0:04:11.158,0:04:13.903
And our lines[br]don't have to be straight.

0:04:14.389,0:04:17.304
They can curve to fit the data[br]when necessary.

0:04:17.770,0:04:21.262
This line also gives us[br]a way to predict outcomes.

0:04:21.579,0:04:25.569
We can simply take a beauty score[br]and read off the line

0:04:25.569,0:04:28.429
what the predicted[br]evaluation score would be.

0:04:28.609,0:04:30.546
So, back to our new professor.

0:04:31.097,0:04:34.109
We can precisely predict[br]his evaluation score.

0:04:34.683,0:04:36.749
"But wait! Wait!" you might say.

0:04:37.019,0:04:38.749
"Can we trust this prediction?"

0:04:39.233,0:04:41.665
How well does[br]this one beauty variable

0:04:41.665,0:04:43.515
really predict evaluations?

0:04:44.844,0:04:47.890
Linear regression gives us[br]some useful measures

0:04:47.890,0:04:49.770
to answer those questions

0:04:49.770,0:04:52.039
which we'll cover[br]in a future video.

0:04:52.838,0:04:55.439
We also have to be aware[br]of other pitfalls

0:04:55.439,0:04:58.340
before we draw[br]any definite conclusions.

0:04:58.833,0:05:00.430
You could imagine a scenario

0:05:00.430,0:05:03.639
where what is driving[br]the association we see

0:05:03.639,0:05:06.900
is really a third variable[br]that we have left out.

0:05:07.344,0:05:09.965
For example,[br]the difficulty of the course

0:05:09.965,0:05:12.456
might be behind[br]the positive association

0:05:12.456,0:05:15.645
between beauty ratings[br]and evaluation scores.

0:05:16.052,0:05:18.956
Easy intro. courses[br]get good evaluations.

0:05:19.228,0:05:22.972
Harder, more advanced courses[br]get bad evaluations.

0:05:23.660,0:05:27.668
And younger professors might[br]get assigned to intro. courses.

0:05:28.080,0:05:32.095
Then, if students judge[br]younger professors more attractive,

0:05:32.095,0:05:34.335
you will find[br]a positive association

0:05:34.335,0:05:37.383
between beauty ratings[br]and evaluation scores.

0:05:37.861,0:05:40.388
But it's really[br]the difficulty of the course,

0:05:40.388,0:05:43.537
the variable that we've left out,[br]not beauty,

0:05:43.537,0:05:45.848
that is driving evaluation scores.

0:05:46.346,0:05:49.807
In that case, all the primping[br]would be for naught --

0:05:50.289,0:05:54.441
a case of mistaken correlation[br]for causation,

0:05:54.900,0:05:58.166
something we'll talk about further[br]in a later video.

0:05:58.922,0:06:02.069
And what if there were[br]other important variables

0:06:02.069,0:06:05.781
that affect both beauty ratings[br]and evaluation scores?

0:06:06.626,0:06:09.575
You might want to add[br]considerations like skill,

0:06:09.846,0:06:14.577
race, sex, and whether English[br]is the teacher's native language

0:06:14.577,0:06:18.994
to isolate more cleanly the effect[br]of beauty on evaluations.

0:06:19.408,0:06:21.758
When we get[br]into multiple regression

0:06:21.758,0:06:24.477
we will be able to measure[br]the impact of beauty

0:06:24.477,0:06:26.219
on teacher evaluations

0:06:26.219,0:06:28.368
while accounting[br]for other variables

0:06:28.368,0:06:30.737
that might confound[br]this association.

0:06:31.762,0:06:35.509
Next up, we'll get our hands dirty[br]by playing with this data

0:06:35.509,0:06:39.070
to gain a better understanding[br]of what this line can tell us.

0:06:41.169,0:06:42.445
- [Narrator] Congratulations!

0:06:42.445,0:06:45.247
You're one step closer[br]to being a data ninja!

0:06:45.568,0:06:47.139
However, to master this

0:06:47.139,0:06:48.700
you'll need[br]to strengthen your skills

0:06:48.700,0:06:50.404
with some practice questions.

0:06:50.865,0:06:53.976
Ready for your next mission?[br]Click "Next Video."

0:06:54.313,0:06:55.364
Still here?

0:06:55.598,0:06:58.325
Move from understanding data[br]to understanding your world

0:06:58.325,0:07:01.642
by checking out MRU's[br]other popular economics videos.

0:07:01.892,0:07:04.406
♪ [music] ♪