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In this video, we will introduce

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the Fundamentals of
regression analysis,

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which we believe is
the workhorse of

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statistical analysis.

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Now, in terms of
hypothesis testing,

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these tests measure
the strength of

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relationship between
two or more variables.

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And you have to run
them independently.

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But if you know how
to run regression,

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we say, as a practical
data scientist,

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you can forego these tests and
go straight to regression,

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which is available in

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most spreadsheets and also
in all statistical software.

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So here the fundamental
basics of regression model.

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First of all, you need a question

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to answer using regression model.

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For instance, do
male instructors get

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higher teaching evaluations
than female instructors?

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Or does the beauty score decrease

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with the aid of the
individual instructor?

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Or is there an
association between

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an instructor's looks and

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the teaching evaluation
score that we see?

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Do good-looking professors get

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hired teaching evaluation scores?

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So with these questions in mind,

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we focus now on the terminology
of regression model.

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So there are two types of

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regression variables that we use.

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One is a dependent variable,

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that is the variable that we
are really interested in.

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For example, the teaching
evaluation score

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of an individual instructor and

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the explanatory
variables that explain

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the variance or differences

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of values of the
dependent variable.

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So for example, teaching
evaluation score

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could be explained by the looks,

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or the gender, or

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the English language proficiency

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of an individual instructor.

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So you have two
types of variables,

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dependent and explanatory.

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Now, let's look at the notation
for a regression model.

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The dependent variable
is donated as Y.

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So this Y would be the
teaching evaluation score.

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And the explanatory
variables are denoted as Xs.

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So beauty, the gender and

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English language
proficiency would be an X.

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And the underlying assumption is

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that Y is explained by X,

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that is teaching evaluation
score Y is explained by X,

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that is the beauty score,

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or y is a function of x,

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which we write as Y is
equal to function of X,

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that is, the teaching
evaluation score

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is some function of beauty.

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Statistically, if you run them,

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an estimate, a regression model,

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Y is equal to some constant and

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then a weighting factor
for the variable X.

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If it's a beauty score,

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then the weighting factor for

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the beauty score
and the error term.

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An error term is whatever we
cannot explain by the model,

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that goes into error term.

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And I will explain this a
little more in a minute.

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So Y is equal to,

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let say the constant is

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beta-naught plus some
factor of weight,

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which is beta one for X plus

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the error term which we
represent as epsilon.

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And then if you are familiar with

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your basic statistics text,

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if there are more
than one variables,

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then Y is equal to beta naught,

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that's the constant,
plus beta one, X_1.

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Beta one is the factor for

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one variable that
could be beauty,

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plus beta two the other
weight explaining

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another X_2 and other variables

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such as English
language proficiency.

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So the weight for
English language

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proficiency would be beta

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two and plus the epsilon,

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which is the error term

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explaining or capturing whatever

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the model couldn't capture.

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If I had estimated a regression
model using the data set,

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teaching evaluations data set,

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it would look like the following.

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It will be the teaching
evaluation score of

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an individual instructor
is equal to some

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constant plus the weight for

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the beauty variable and then

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times the beauty
score plus the error.

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So here, teaching evaluation
score is equal to,

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according to the model 3.998.

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That's the constant plus the
weight for beauty score,

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which is 0.133 plus the error.

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And the error is epsilon,

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which is essentially
the difference

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between the actual
teaching evaluation score,

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that we have recorded
in the data set,

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and the one that we have
forecasted using this model.

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So the difference between
the actual values and

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the forecasted values
is the error term.