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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[br]a shiny new tool

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to put into your[br]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[br]how good-looking people

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seem to get special perks.

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

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What about full professors?

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Is it possible[br]good-looking professors

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might get special perks too?

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Is it possible[br]students treat them better

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by showering them[br]with better student evaluations?

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If so, is the effect of looks

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on evaluation score[br]big or [inaudible]?

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

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What can we predict[br]about his evaluation

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simply by his looks?

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Given that these evaluations[br]can determine pay raises,

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if this theory were true[br]we might see professors resort

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to some surprising tactics[br]to boost their scores.

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Suppose you wanted to find out

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if evaluations really improve[br]with better looks.

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How would you go about[br]testing this hypothesis?

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You could collect data.

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

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how good looking a professor was,

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which gives you[br]an average beauty score.

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Then you could retrieve[br]the teacher's teaching evaluations

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from 25 students.

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Let's look at these two variables[br]at the same time

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by using a scatterplot.

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We'll put beauty[br]on the horizontal axis,

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and teacher evaluations[br]on the vertical axis.

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For example, this dot[br]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[br]is Professor Helmchen.

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- [Professor Helmchen][br]Ridiculously good-looking!

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- [Thomas] Who got[br]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[br]on the horizontal axis,

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from the ugly to the gorgeous,

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we see a trend upwards[br]in evaluation scores.

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

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is not made up --[br]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"[br]is just the fancy academic way

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of saying beauty.

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With scatterplots[br]it can sometimes be hard

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to make out the exact relationship[br]between two variables --

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especially when the variables[br]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[br]this bounciness

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is to draw a straight line[br]through the data cloud

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in such a way that this line[br]summarizes the data

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as closely as possible.

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The technical term for this[br]is "linear regression."

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

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but for now we can assume[br]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[br]upward or downward.

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

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It thus confirms what[br]we have conjectured earlier

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by just looking at the scatterplot.

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The upward slope means[br]that there is a positive association

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between looks[br]and evaluation scores.

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In other words, on average,

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better-looking professors[br]are getting better evaluations.

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

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Or, you might see[br]a negative association.

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Or perhaps no association at all.

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And our lines[br]don't have to be straight.

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They can curve to fit the data[br]when necessary.

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This line also gives us[br]a way to predict outcomes.

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

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what the predicted[br]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[br]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[br]this one beauty variable

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really predict evaluations?

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Linear regression gives us[br]some useful measures

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to answer those questions

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which we'll cover[br]in a future video.

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We also have to be aware[br]of other pitfalls

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before we draw[br]any definite conclusions.

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You could imagine a scenario

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where what is driving[br]the association

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

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For example,[br]the difficulty of the course

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might be behind[br]the positive association

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between beauty ratings[br]and evaluation scores.

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Easy intro. courses[br]get good evaluations.

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Harder, more advanced courses[br]get bad evaluations.

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And younger professors might[br]get assigned to intro. courses.

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Then, if students judge[br]younger professors more attractive,

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you will find[br]a positive association

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between beauty ratings[br]and evaluation scores.

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But it's really[br]the difficulty of the course.

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The variable that we've left out,[br]not beauty,

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that is driving evaluation scores.

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

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a case of mistaken correlation[br]for causation,

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

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And what if there were[br]other important variables

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that affect both beauty ratings[br]and evaluation scores?

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You might want to add[br]considerations like skill,

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

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to isolate more cleanly the effect[br]of beauty on evaluations.

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When we get[br]into multiple regression

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we will be able to measure[br]the impact of beauty

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on teacher evaluations

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while accounting[br]for other variables

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that might confound[br]this association.

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

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

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- [Narrator] Congratulations!

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

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

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with some practice questions.

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Ready for your next mission?[br]Click "Next Video."

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Still here?

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Move from understanding eata[br]to understanding your world

9:59:59.000,9:59:59.000
by checking out MRU's[br]other popular economics videos.

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♪ [music] ♪