How to interpret multiple regression
Regression
is useful for making a predictive model. Let's say there's a positive
linear correlation between K
and N,
but you suspect that Factors L
and M
also contribute to Outcome N.
Make up a story—say, that Factors K,
L,
and M
represent intelligence, persistence, and amount of sleep per night
and N
refers to a course grade.
So,
to test the relative impacts of Factors K,
L,
and M
on Outcome N,
you can feed each factor into a regression model, and test whether
each factor increases the fit. That is, a correlation between Factor
K
and Outcome N
yields a Pearson's r
of
.64
and
R2
of
.4096.
But, when you run a regression
testing
the effect of
Factors
K
and
L
on
Outcome N,
you find an R2
of
.5625, with
a
significant change in the R2
value.
That
means
that Factors K
and
L
together
do
a better job of
explaining
the relationship than Factor K
alone.
Then,
you run a regression with Factors
K,
L,
and M
together,
and find
an
R2
of
.5929, with no significant change—this
means that Factor M
does
not help
to
explain the relationship.
Outcome
N
is
due mostly to Factors K
and
L;
Factor M
is
an
unimportant
predictor
of
Outcome
N.
Voilà! There's regression in a nutshell!
And, if you're confused about the math...remember in middle school or high school math, when you learned about "rise over run" and learned the formula y = mx + b? Yeah, that's a simple linear regression. With multiple regression, you can add multiple terms, such that y = ax1
+ bx2 + cx3...+ z. But it's still the same concept, just with more predictors than that lone "mx" term.
For more help explaining statistical concepts and when to use them,
In case you missed it, there are some fantastic, easy-to-use, and FREE stats programs available now! I review them here.
please download my freely available PDF guide here!
