Mean centering in regression in SPSS Video Lecture | SPSS: For Beginners - Data & Analytics

hi everyone Phil from Statistics mentor
calm here and in this video we're going
to be discussing about how to alleviate
multicollinearity in a polynomial
regression model by using mean centering
method recall multicollinearity is
situation where we have a high degree of
linear relationship among the IV's in
the model and this could result in
coefficients on the slope parameters
which appear to be insignificant when
actually they should be significant now
there are many ways to deal with
multicollinearity the mean centering is
one such method and the mean centering
method works well when we have a
polynomial regression model that is one
in which that we have powers of the iv2
terms involving powers of the IV so in
this example we've got as a DV earnings
and we've got earnings at salary and ids
we've got years of working experience
and we've got experience squared okay so
these are the two IVs in this model if
we regress earnings on experience and
experience squared that's a polynomial
regression because we have a power term
on one of that on the IV squared term in
this case then we would expect there to
be able to karate because these two are
related
now let's fit the regression first
depend variable earnings experienced
experienced squares IVs and we look for
the colonizer statistics okay go down to
the table that says coefficients here we
go now the vif measure
recall that the vif is telling us that
multi-character is a big problem if the
number here is exceeds ten so here two
hundred nine ten massive so there is a
problem if also if we look in addition
if we look at the T statistics for these
two IVs coefficients and IVs we find
that both in significant but then that's
one of the code one of the symptoms of
multiple of multicollinearity right now
if we look at the correlation we will
see what the problem is so experience
experience squared we want Pearson's
correlation between experience and
experience squared is very close to one
point nine nine eight and significant
okay that's why we've got this problem
or multicollinearity in this model okay
well since it's a polynomial regression
one waited to leave it multicollinearity
is to use mean century now by means
centering what we do is we take the IV
and we subtract off it the mean now for
the experience we need to find out what
the mean is so if we go to the
descriptive stats say descriptives
experience options let's just pick out
the mean I get rid of it take everything
else the mean is about nineteen point
four seven nineteen point four seven so
what want to do next is we want to
compute a new variable let's call it C
Expo for centered percent experience and
what we want to do is that experience -
and then the mean which we found to be
nineteen point four seven there abouts
nineteen point four seven okay
now we've got a new column and what want
to do is want to create the experience
squared as well but we want to do with
the transformed the mean transform one
so in other words I am going to take
centered experience and square that to
get the centered experience squared I am
NOT taking the experience squared and
subtracting the mean of this column all
right two different things so transform
let's call the new variable CX square
and it is made up of CX it made up of C
it all squared like so I've got two new
columns want to do now to regress
earnings on on the center experience and
send it experience squared all squared
of centered experience you analyze
regression linear take these two out and
place them by the centered versions so
we still have the that was a mistake sir
we should still have the : sure
statistics that show you that the
problem has been reduced or if not
eliminated so here's the output
fantastic right if we look at this you
can see now that the coefficients table
that's what's the centered versions of
the IV's the vif is now way below 10
practice about 1.3 so it's no longer an
issue okay if we look at the correlation
of the centered versions of Ivy's
should find that they've been reduced as
well yes look it's gone way down to
about 0.5 ish point - point four eight
five in other words what this means
centering has done is it has reduced the
correlation it's also change the sign of
a thing isn't it
all right let's think that so for
polynomial regression we can reduce
multicollinearity or alleviate it by
using the mean centering now this means
entering does it always work for any
kind of regression model it tends to
work best for polynomial regression if
you try it okay so it's not polynomial
regression you find that it works
doesn't work that well if at all okay
but there are people who just use it
whenever they see multicollinearity so
what we know is that we shouldn't do
that we should just works best for
polynomial regression and there and for
if it's not polynomial regression we
should look at other things finally to
finish off with these coefficients now
have a slightly different meaning
okay the two usual one unit increase in
next leads to a blah blah' unit increase
in Y holding everything else fixed the
constant here 22.7 that will be the
predicted earnings when the experience
for that particular person is equal to
the to the mean value of nineteen point
four seven
the interpretation of the coefficient on
the centered experience of 0.94 four
would be if the person is earning if
persons work work experience is around
the mean of nineteen point four seven
then for an additional year of work
experience that person can expect the
the earnings to increase by 0.9 for four
units whatever those units are of
measurement of earnings okay so they're
only holding everything else fixed so
the only difference here is that we're
not saying one unit increase in X leads
to blah blah blah we're saying the one
unit increase in X if that X is close to
the mean all right for the squared term
here a minus sign means that we've got
diminishing returns on earnings in other
words for an additional year of
experience at the rate of the rate of
increase on the as earnings slows down
okay so that is means entering for the
deal with multicollinearity in a
polynomial regression model antastic
let's finish there