SPSS for newbies Standardized residuals in regression when the residuals

see hi everyone this is Phil from
statistics mentor.com
what like to address is where the
standardization works four variables are
not normally distributed we call that
when we first see standardization we use
the told that the variable is normally
distributed with mean which is not zero
in a variance wisdom which is not one
standardization is a process which we
get that's variable into a new variable
called Z which is normally distributed
with mean of 0 and a variance of 1 now
I'd like to know whether this
standardization process works when your
variable is not normally distributed why
that might that be an interesting
question might be interesting in the
case of regression because once we do a
regression and we look at residual plot
we know that we should look at the
standardized or studentized residuals
rather than the normal residuals but if
my residuals are not normally
distributed does it make sense to
standardize them we're going to look in
this video we got education data here DV
is earnings IB is workers working
experience to their favorite regression
analyze regression linear earnings
interdependent Bucks experience into the
independent box and then we go save
we're going to save the unstandardized
residuals and the standardized because
we want to look at the shape of the
distribution is it normal or not to new
ok so here we have two new columns one
of the unstandardized residue the plain
old raw residuals and the standardized
residuals now let's look at the shape of
this here residual the raw residuals
graph I'm going to choose to use the
legacy dialogues histogram visit into
the variable box ok
what we can see from this is that the
residual plot
sorry not residual plot the histogram of
the unstandardized residual has a mean
of close to 0-8 point times 10 to minus
15 so 2 plus 0 but the standard
deviation is not 1 it's 14 moreover this
distribution is certainly not
symmetrical it is positively skewed so
when we go and compute the standardized
versions as we've asked SPSS to do will
it will this column have a mean of 0 and
a variance of 1 and will it what will be
the shape of the distribution let's have
a look graph legacy dialogues histogram
sit standardized residuals instead
here it comes standardized residuals
histogram of the standardized residuals
is it normally distributed no it is
still positively skewed what about the
mean the mean is -5 times 10 to minus 16
that's pretty much zero
how about sender you Gatien point nine
eight seven that's pretty much close to
one in other words standardization has
worked even though my distribution is
not normally my variable is not normally
distributed okay so I brought this up is
that when wherever when typically
students are presented with this process
standardization that it's done in
context that the variable is normally
distributed but here I've shown you that
works even when the variable is not
normally distributed we might encounter
such an occasion to see this when we're
doing linear regression and now
residuals are not normally distributed
but then standardization still works and
we need standardized residuals just hunt
for things such as outliers okay nice
brief tutorial and I hope this has been
useful to you