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PROFESSOR: Hello, and welcome.
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In this video, I'll explain to
you what multicollinearity is
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and how you can check it online.
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And we get started right now.
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So the first question is,
what is multicollinearity?
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Multicollinearity means that two
or more independent variables
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are strongly correlated
with one another.
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The problem about
multicollinearity is that
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the effect of individual
variables cannot be clearly
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separated.
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Let's look at the
regression equation again.
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We have the dependent
variable here
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and the independent
variable with
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the respective coefficients.
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For example, if there is a high
correlation between x1 and x2,
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or if these two variables
are almost equal,
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then it is quite difficult
to determine b1 and b2.
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If both variables
are completely equal,
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the regression model does not
know how to determine b1 and b2.
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This means that the regression
model becomes unstable.
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If you now want to
use the regression
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model for a
prediction, it does not
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matter if there is
multicollinearity.
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In a prediction, you are
only interested in how good
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the prediction is,
but you are not
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interested in how
big the influence
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of the respective variables is.
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However, if the regression model
is used to measure the influence
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of the independent variable
on a dependent variable,
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there must not be
multicollinearity, and if it is,
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the coefficients cannot be
interpreted meaningfully.
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So the next question
is, how can we now
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diagnose multicollinearity?
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If we look at the
regression equation again,
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we have the variable x1, x2,
and upon to the variable xk.
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We now want to
know if x1 is quite
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identical to any other
variable or a combination
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of the other variables.
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In order to do this, we simply
set up a regression model.
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In this new regression
model, we take x1
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as the new dependent variable.
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If we now can
predict x1 very well
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from the other
independent variables,
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we don't need x1 anymore,
because we can use
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the other variables instead.
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If we would now
use all variables,
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it could be that the regression
model gets very unstable.
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In mathematics, we would
say that the equation
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is overdetermined.
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We could now do this
for all other variables.
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So we estimate now x2 by
using the other variables.
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And we estimate xk by
the other variables.
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In this case, we have k
new regression models.
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For each of these
regression models,
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we calculate the tolerance and
the variance inflation factor.
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The tolerance is obtained
by taking 1 minus r squared,
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which is the coefficient
of determination
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or the variance explanation.
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The variance
inflation factor is 1
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divided by 1 minus the
coefficient of determination.
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Multicollinearity could
exist if the tolerance
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is smaller than 0.1.
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If we look at the
variance inflation factor,
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there could be multicollinearity
if the variance inflation
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factor is larger than 10.
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And now I will show
you how you can easily
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check the requirements online.
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In order to do this,
please visit datatab.net,
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and click on the
Statistics Calculator.
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If you want to use your own
data, just click on Clear Table.
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I will use the example data now.
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If you want to
perform a regression,
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just click on the
tab Regression.
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On the left side, you can
choose your dependent variable.
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On the right side,
you can choose
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your independent variables.
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In our example, we
want to choose salary
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as the dependent variable.
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And as the
independent variables,
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we choose gender,
age, and weight.
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Now we can click on
Check conditions.
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And we get the results
of the condition checks.
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First, we start
with the linearity.
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Then we see the
normality of errors.
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Further, we have the
multicollinearity tests,
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where we have the tolerance and
the variance inflation factor.
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And finally, we can see the
test of homoscedasticity.
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This is how easy you can
check the requirements
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for a linear regression model.
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Another important topic when
talking about regression models
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are dummy variables.
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If you want to learn more
about dummy variables,
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just continue to
watch the next video.
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See you soon.
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