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Intro to Linear Regression

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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,
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    "Where else might we see
    this phenomenon?"
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    What about for 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 evaluations really big
    or really small?
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    And say there is a new professor
    starting at a university.
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    - [man] G'day, mate.
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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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    - [Lloyd Christmas] Yeah!
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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 twenty-five 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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    - [Bib Fortuna] De wana wanga.
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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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    - [Ben Stiller, "Zoolander"]
    Ridiculously good-looking!
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    - 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 values
    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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    - [Lloyd] Look familiar?
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    - 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 we see
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    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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    - [Lloyd] Wait a minute.
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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
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    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 data
    to understanding your world
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    by checking out MRU's
    other popular economics videos.
  • 7:02 - 7:04
    ♪ [music] ♪
Title:
Intro to Linear Regression
Description:

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Video Language:
English
Team:
Marginal Revolution University
Project:
Understanding Data
Duration:
07:05
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Kirstin Cosper edited English subtitles for Intro to Linear Regression
Kirstin Cosper edited English subtitles for Intro to Linear Regression
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