In this video, we will introduce
the Fundamentals of regression analysis,
which we believe is the workhorse of
statistical analysis.
Now, in terms of hypothesis testing,
these tests measure the strength of
relationship between two or more variables.
And you have to run them independently.
But if you know how to run regression,
we say, as a practical data scientist,
you can forego these tests and go straight to regression,
which is available in
most spreadsheets and also in all statistical software.
So here the fundamental basics of regression model.
First of all, you need a question
to answer using regression model.
For instance, do male instructors get
higher teaching evaluations than female instructors?
Or does the beauty score decrease
with the aid of the individual instructor?
Or is there an association between
an instructor's looks and
the teaching evaluation score that we see?
Do good-looking professors get
hired teaching evaluation scores?
So with these questions in mind,
we focus now on the terminology of regression model.
So there are two types of
regression variables that we use.
One is a dependent variable,
that is the variable that we are really interested in.
For example, the teaching evaluation score
of an individual instructor and
the explanatory variables that explain
the variance or differences
of values of the dependent variable.
So for example, teaching evaluation score
could be explained by the looks,
or the gender, or
the English language proficiency
of an individual instructor.
So you have two types of variables,
dependent and explanatory.
Now, let's look at the notation for a regression model.
The dependent variable is donated as Y.
So this Y would be the teaching evaluation score.
And the explanatory variables are denoted as Xs.
So beauty, the gender and
English language proficiency would be an X.
And the underlying assumption is
that Y is explained by X,
that is teaching evaluation score Y is explained by X,
that is the beauty score,
or y is a function of x,
which we write as Y is equal to function of X,
that is, the teaching evaluation score
is some function of beauty.
Statistically, if you run them,
an estimate, a regression model,
Y is equal to some constant and
then a weighting factor for the variable X.
If it's a beauty score,
then the weighting factor for
the beauty score and the error term.
An error term is whatever we cannot explain by the model,
that goes into error term.
And I will explain this a little more in a minute.
So Y is equal to,
let say the constant is
beta-naught plus some factor of weight,
which is beta one for X plus
the error term which we represent as epsilon.
And then if you are familiar with
your basic statistics text,
if there are more than one variables,
then Y is equal to beta naught,
that's the constant, plus beta one, X_1.
Beta one is the factor for
one variable that could be beauty,
plus beta two the other weight explaining
another X_2 and other variables
such as English language proficiency.
So the weight for English language
proficiency would be beta
two and plus the epsilon,
which is the error term
explaining or capturing whatever
the model couldn't capture.
If I had estimated a regression model using the data set,
teaching evaluations data set,
it would look like the following.
It will be the teaching evaluation score of
an individual instructor is equal to some
constant plus the weight for
the beauty variable and then
times the beauty score plus the error.
So here, teaching evaluation score is equal to,
according to the model 3.998.
That's the constant plus the weight for beauty score,
which is 0.133 plus the error.
And the error is epsilon,
which is essentially the difference
between the actual teaching evaluation score,
that we have recorded in the data set,
and the one that we have forecasted using this model.
So the difference between the actual values and
the forecasted values is the error term.