SPSS for newbies: 1 multiple regression is not the same as running many simple linear regressions Video Lecture | SPSS: For Beginners - Data & Analytics

hello everyone Phil from Statistics
mentor.com today I want to discuss the
need for multiple regression recall that
regression there are standard regression
model the two basic ones the simple
linear regression model and the multiple
linear regression model any course in
stats or econometrics we always begin
with the simple linear regression model
recall this is the model where there is
a dependent variable denoted generically
by Y and there is one independent
variable denoted by X that's a generic
formula symbol so there is only two
variables in the simple linear
regression model 1 Y and 1 x for the
multiple linear regression model there
is more than one independent variable so
is - all there are two or more okay well
my question to you is since the simple
linear regression model is the simplest
simpler than the multiple why don't we
just use that all the time let us give
you an example
I've got data on health care here my
about three variables my dependent
variable my DV is the report to disease
rate rate per 10,000 I just want to see
whether if the government puts more
money into health care whether the
disease rates comes down we'd expect it
should come down also how about visits
to health care providers how would that
be related to the diseases well we kind
of think that the more people visits to
healthcare providers more people who
visit health care providers reported
disease rates should go up I were expect
a positive correlation there there's
more people who visit probably more
chance of detecting more disease more
people more disease between health care
funding and reported disease we would
expect a negative correlation because
the more money they put into healthcare
we expect that to help improve the
health care system and so the report
disease rate should come down see so
this is not statistics it's just using
kind of common sense right so why don't
we fit two simple linear regression
models one regressing the disease on
healthcare funding and one a second
model of disease on visits to health
care providers so try to separate saying
simple linear regression models let's do
that regression linear I take the
disease rate into a dependent variable
let's do funding first and move that
into independent variable box
click ok right want to go straight down
to the coefficients table here the beta
4 slope coefficient for the independent
variable is here okay Oh what you can
see is that it is positive so that
saying that as that there is a positive
correlation between healthcare funding
and reported disease rates that's
contrary to what we'd expect so this is
saying that the more money we because
it's a positive sign here positive 1.13
for the more money we put into
healthcare the higher the reported
disease rates contrary to what we'd
expect and what explain to you in a
moment why we get this sign a positive
sandwich is contrary to what we'd expect
now let's do the same but with the other
independent variable analyze regression
linear funding take that away visits
take that in before we look at the
output recall that we said expects a
positive correlation so we expect there
to be a positive slope coefficient so
let's go down right so this is the
health care providers it's positive and
coefficients positive 1.0 for 8 and now
so wicks expected a positive sign we get
a positive sign this is saying that the
increase for it for increases in the
visits to health care providers we get
an increase in reported disease rates
right so let's pause and reflect
in the first simple linear regression we
found a result country to work expected
but in the second one of disease rates
on health care providers we got the
expected sign now how kind of we
explained the unexpected sign for the
first regression right well the key is
this it is that if the dependent
variable depends on more than one key
independent variable those independent
variables should go into the model
together so in this case if we think
that disease rate depends on healthcare
funding and the number of visits to
healthcare providers we must put both
those independent variables into the
same model failure to do that if we
think that we can try just running them
one by one I just run instead of a
multiple regression we've run separate
simple linear regression models our
coefficients are liable to be wrong in
so obey either too high or too low in
statistical jargon we say that these
coefficients are biased okay so if I
summarize this lesson nutshell it is
that a simple linear regression model
cannot take the place of multiple
regression model where multiple
regressions should be running we should
not just run separate simple linear
regression models if we do so we get
biased estimators
that's the lesson there is one exception
which you don't need to take this on
board because for real life data is
probably not not applicable
theoretically week instead of running a
we can get by my running simple linear
regression models separate ones instead
of multiple ones if the independent
variables are uncorrelated zero
correlation so in this case what I mean
is to say that we got two independent
variables we've got two let's go just go
back we've got funding and visits now if
funding and visits are uncorrelated of
zero correlation then instead of running
a multiple regression of disease on
funding and visits we can run them
separately on disease and funding
disease and visits in that case we were
to get unbiased estimators okay so even
if so even if the question was that I'm
interested in looking at the effect of
funding on disease and I'm not really
interested in the visits on disease
because visits also effects disease we
should include it even though we're not
interested in its impact on disease okay
for that reason such variables which for
which we are not interested in but we
have to include them otherwise because
we have otherwise we get biased
estimators for coefficients I'm
interested in coefficients on the
variables I'm interested in these extra
variables that we must include are
called control variables okay it's
control variables we were not interested
in them per se but one must include them
because otherwise the coefficients on
the on the IV that we're interested in
likely to be biased alright so why don't
we now run a multiple regression model
and see how things changes I will put
both funding and visits now so we're
going to run a this becomes now multiple
regression so we have two independent
variables so we have two beaters here
see alright so say I'm specifically
interested in the effects of healthcare
funding on disease rates we can see now
look that the coefficient is closer to
zero healthcare funding zero moreover is
insignificant meaning that it's not
significantly different from zero
meaning corn to this model healthcare
funding does not impact it's not a
predictor for reported disease so before
it was very positive now it's come right
down it's got closer to zero so we go
back to the start it was one point one
three four now it is not point naught 5
which is close to zero look at the
control variable visits to health care
providers it's positive as before you
can imagine but still positive but but
actually it's different it's a zero it's
not significantly different from zero
you can imagine that there other control
variables that we might include here and
if we find those other control variables
this could well come down to be negative
so in other words this model here is
probably still not adequate
but the degree of bias is will expect is
a smaller now than before when we look
at the simple linear regression models
okay well so don't make that mistake if
you need multiple run multiple don't run
simple in practice especially for
example Social Survey data experiments
you in real life you only simple linear
regression models to help you understand
how regression works but they're rarely
applicable in the real world so you
should always be thinking multiple
regression okay take care