SPSS for newbies Interpretation of the coefficients in regression when

hello everyone Phil from Statistics
mentor.com here today we're going to be
discussing about how the interpretation
of the coefficient changes when we use
log transform in regression first I'm
going to present the basic results so
interpreting the coefficients on the IV
now we're going to for simplicity
consider the simple linear regression
model but is it's pretty easy to kind of
review why's that for multiple
regression so case 1 DV no log transform
no transformation IV has no
transformation then the interpretation
of the coefficient on the IV is the
model predicts that a one unit increase
in the IV leads to an increase or
decrease in the DV by beta units where
we replace the word unit by whatever
unit of measurement is being used for
the IV increase or decrease we choose
which one ever one of those matches the
sign on the coefficient so if the sign
of the coefficient is positive we would
say lead to an increase of the sign on
the coefficient is negative we will say
decrease in the DV by beta units betas
are actual number which you get from the
SPSS output that is the coefficient on
the IV this is a standard one that we
see in our first regression model now
transformation why would we the common
transformation is taking a log transform
we might take a lot transform off the DV
we might take log transform with the IV
we might take transform of both IV and
DV why would we take log transform well
sometimes by taking log transform we can
help to link to normalize the residuals
or the error disturbance term
which is required for many tests another
reason is that the model the original
model may not be linear they not be it
may not be a linear relationship between
these between the DV and the IV and by
taking locks we can kind of linearize it
we can make it linear in the parameters
stroke coefficients right then so with
that background let's look at the first
case
well next case we take the log say we
want to take the log of the DV and we
take the log of the IV how does that
affect the interpretation of the
coefficients it becomes this the model
predicts that a 1% increase in IV or X
keep it concealed leads to an increase
or decrease in the DV by beta percent so
the words units have been replaced by
percent this makes the interpretation
quite nice because you know when we talk
of a scented terms everything is easier
to kind of understand rather than I the
IB indeed in different units next DV is
transformed using log IV no
transformation in this case the
interpretation of coefficients on IV is
this the model predicts that one unit
increase in IV leads to an increase or
decrease in the DV by 100 times that
number beta and then it's in percentages
final one no transform on the DV log
transforming the IV we would say that
the coefficient on the IVs we interpret
like this the model predicts that a 1%
increase in the IV leads to an increase
or decrease in DV by the beta value
divided by 100 units
so these things cases you jot down on a
piece of paper and then we're now going
to apply it to an example simple linear
regression I'm going to use education
data so my DV will be earnings and the
IV will be work experience here we go
the earnings is measured in thousands of
dollars say work experience is measured
in years
first let's do it with a no
transformation on the either DV or IV
regression linear V DV okay go straight
down to the coefficient box
interpretation on the IV where
coefficient is 1.04 seven so what would
say is for an extra additional year of
work experience the model predicts that
the earnings will increase by one
thousand forty seven dollars extra times
this by one thousand one thousand and
forty seven dollars another way of
saying it is the model predicts that for
one at one unit one year increase in the
work experience the earnings were
increased by one thousand forty seven
dollars okay next let's do the log log
transform now recall that we cannot take
logs of numbers which are not zero or
below so all my earnings and all my
experience there will flick through none
of them are zero or negative so we can
take a log transform transform so we
want to transform compute variable and
where I create logs so let's say I'll
earn for log earnings and here we will
do
log which could tap straight in L and
open bracket and closed brackets okay
that and also do the same for the IV
experience I'll explore lot of
experience place in here
the name log experience okay so now
let's regress log Burns on log
experience analyze aggression linear
reset to clear the window log earnings
in the dependent log experience into
independent I'd say okay but here's the
coefficient box here's the coefficient
on log of experience point 793 so the
interpretation is this the model
predicts that for 1% increase in
experience the earnings will increase by
0.793 percent about point eight percent
simple as that
next let's do log of dependent variable
and linear of no load transformation on
the IV so regression log of earnings on
experience so we're logging the
dependent we're not logging the IV
coefficients the coefficients on the IV
is 0.04 three so we say let's just go
back log here so what we have to do is
times the beta by 100 alright so what
say is that the model predicts that if
the work experience increased by one
year the earnings will increase by times
by 100 four points
3% okay 4.3 percent
and finally just straight forward you
see once you've got the table in front
of you we do earnings which is not
logged and we will log the IV okay the
coefficient is nineteen point four eight
go back to our table we are not logging
that DV we are logging the IV so what we
try petition here is we have to divide
the beats by 100 and then units okay so
what we say is the model predicts that
if the work experience increases by one
percent then the the earnings will
increase because it's got positive there
by this divided by hundred which is
about point one nine by point one nine
four to eight thousands of dollars huh
but to say we could leave it there but
that's not so natural 0.194 to eight
thousands of dollars is same as saying
times it by one thousand one two three
one hundred and ninety-four dollars get
that okay so we've talked about
performing log transformation in
regression and we've talked about how
that we've talked about the
interpretation of the coefficients when
we use the log transformation on the DV
and IV we noted that the log
transformation can be applied to numbers
which are not to look not zero on below
zero
okay however if you have numbers at zero
or below zero one way to get around it
is you scale everything up by adding a
constant to every single value in that
variable in that data so for example if
earnings here was instead of some reason
zero that person is not working or
something we could scale it up by adding
to everything along down this column one
because then that would get rid of the
problem of zero okay and it's theory to
show you why that surely works ok well
fantastic this is commonly a kind of
employed technique and hope you make use
of it ok all for now