SPSS for newbies: Why having a high R-squared in regression could be a bad thing Video Lecture | SPSS: For Beginners - Data & Analytics

hey hi everyone this is Phil from
Statistics mentor comm today I'm going
to talk about this measure called R
squared which no doubt you've heard
about now I find that students when they
first out in stats plays far too much
emphasis on this R square measure they
think that to get a great model they
must come up with a R square of not
point 9 or higher we call that a square
is on a scale from 0 to 1 1 meaning that
it's a perfect fit
I want to explain to you that high R
square could actually mean that you've
got a poor model far from being a good
model first I want you to review the
uses of regression now why do you build
a regression model well there are two
reasons for building a regression model
one is to examine the relationship
between the IV and the DV we do this by
interpreting the coefficients so with
the coefficients we can measure the
sensitivity of changes in DV with unit
change in the IV another use is to use
the model to make predictions so given a
value of the eye of the IV's what does a
model predict to be the D value of the
DV now a high value for the R square
means that the model is useful for
prediction
but not necessarily for interpreting the
coefficients so if your task is for
prediction then you by all means try to
achieve a high R square but if your aim
is or to predict to to interpret the
coefficients your emphasis is not so
much on the R square but more on the
signs and magnitudes of the coefficients
using theory whether it's a cycle
psychology or economics or engineering
theory to come up with a model where you
choose a set of Ivy's predicted by your
theory that should help predict the divi
now I've got example data here to show
you that the R square can be misleading
using the R square can be misleading in
selecting final model so here I've got
Social Survey data on factors that can
influence your well-being so DV is
degree of happiness let's fit a
regression model analyze regression
linear happy in the dependent variable
box in the independent variable box we
can select let's see age say what else
you will are you married
let's put those to it so we're doing a
multiple regression because there are
two IVs all right we'll look at the a
square point one nine six let's see if
we can make that higher analyze
regression linear let's put another one
education else what time spent leisure
let's put those two in okay what's a
square done now
so it's gone up from 0.196 to 0.199
let's see if we can make it go even
higher analyze regression linear let's
see okay putting social and TV in there
okay now the R square is jumped up to
0.366 looking great if we're looking at
just the R square
now let's now let's sir put in this ID
here called Lu which means the average
number of times the person goes to the
loo washroom
a day let's put nine well the R square
has now gone up to pop is now 0.36 9 so
the introduction of the Lu has pushed up
the R square by approximately 1% which
seems a bit absurd if you think about it
wouldn't expect the number of times you
visit the loo to influence your
happiness so I want to point out here is
that the disadvantage of R square is
that if you put in rubbish as Ivy's the
R square will tend to stay the same or
increase it will not decrease so in
other words you put in any old rubbish
into your model more and more rubbish
you put in the R square is just going to
be pushed up arbitrarily towards one and
that if you're looking at a square will
kind of give you a kind of peace of mind
that you are building a great model
but if we look at the coefficients here
we can see several of them are not
significant age level of education upon
to have a hobby
another two there you see by including
more and more Ivy's in your model you
are making the model more susceptible to
what is called multicollinearity which
is a problem it means that there's a
high degree of linear relationship among
the Ivy's and that means that your these
coefficients when the effect is that the
coefficients will become very unstable
and that in effect means that the the
actual numbers here are dubious so you
cook the coefficients I can't be relied
upon so much okay so to recap at this
point I point out the danger of using
high R square R square PI R squared does
not mean that your model is necessarily
good while it may be okay for prediction
coefficients of the interpretation may
be may be spoiled this a square has a
drawback in that the more more Ivy's you
including the model this a square will
be pushed up closer and closer to one
making you think that your model is
improving if you do come up with model
over there high R square then person and
you are really lucky or there is
something else that is wrong with your
model depending on the subject field
what is high in terms of a score what is
a high value for the R square it really
depends on the subject area for the
psychology and Social Sciences
you know hi r-square won't be as high as
for some of the safe physical sciences
such as engineering because there's just
a lot more uncertainty in in dealing
with say people rather than with
machines right so now pointed out the
drawback of our R squared what about
this thing called adjusted r-square well
adjusted r-square does not have the
drawback of R square so historically a
score came first then followed by it
just at our square and the difference is
that just that a square also measures
the same measure of what a square
measures looks on a scale of 0 to 1 but
just the doubt squared penalizes for the
inclusion of irrelevant IVs so if you
put in rubbish IVs the ass just a square
or full cut if you look at it it's
smaller than our square figure here I'll
square for this model is 0.36 95
adjusted r-square is 0.2 75 a rule of
thumb is that if the difference between
a square adjusted R square is greater
than 2 or 3% it suggests that there is a
you've included irrelevant IVs but we
can test for that formally using things
such as a t-test that you can see down
here or we could even use the F test to
test a subset of the IV's coefficients
in IVs so for measuring the goodness of
fit we're going to use it a square
measure then the multiple regression
we're better off reporting the adjusted
r-square
but the fact still remains we're not
after necessary model with massively
high R square adjusted r-square if our
purpose is to explain the relationships
between IV and the DV
okay so next time when you've come up
with a model where the coefficients make
sense and conditions for the regression
are satisfied and don't be too concerned
if your R square adjusted r-square
doesn't seem so high