SPSS for newbies: Interpreting the basic output of a multiple linear regression model Video Lecture | SPSS: For Beginners - Data & Analytics

everyone Phil from Statistics mentor.com
in this video we're going to talk about
the absolute basic output of running the
multiple linear regression model as an
example we've got a Deepak variable
earnings of the independent variables
we've got experience in working say
measured in years and schooling number
of years of schooling let's say to keep
things well earnings that say is
measured in thousands of dollars so the
units is earnings in thousand dollars
experience is in years schooling is in
years we wish to regress earnings on
experience and schooling which means
that taking experience in schooling as
IBS and earnings as the DV so in short
we say jargon is to say it will regress
the earnings on experience and schooling
okay to do it go to analyze regression
linear transfer it into the dependent
variable box the earnings and into the
independent variable box the two IVs
notice there are some options and
statistics and plots available to us
we'll ignore those we'll go okay okay
first box isn't doesn't interest us at
all just tells us what has what IVs are
that are in the model right model
summary this box contains the R square
now for multiple regression we wish to
report and look at the adjusted r-square
rather than the R square and recall that
the R square stroke adjusted R square
measures the proportion of
the total variability in the DV that is
explained by the IV's the model so here
we could report since it's just it R
square is about 0.189 we can report that
about to convert into percentages 19% of
the total variability in earnings
explained by the model or if they've
seen the model we can say that 19% of
the total variability in earnings is
explained by experience and schooling
okay now doesn't mean the R square is
not useful here if there's a big
discrepancy between R Square and
adjusted R square it suggests that some
of the IV's were included in the
regression model is redundant okay
but it's not really good way there's a
more precise way of checking whether
that's the case whether we've included
more Ivy's and we need to as we shall
see shortly then we'll come on to the
two tests and they're following two
tables and all the table presents the
key thing here is the F statistic the F
test and how we get this figure here
five point five three seven is using
these three columns alright so it as a
means to an end all these three columns
where nitrous interesting those figures
are interesting these two final figures
which obtained from the first three now
bigger test we think that apply
statisticians just need to know what is
the null and the alternative the null
hypothesis always for this F testing and
all of the regression is that the model
has no explanatory power which is same
as saying that all the coefficients on
the Ivies is zero but that's the same as
saying that none of the IV's helped to
predict the DV
in other words model is useless all
right
is it do we reject the null or not
reject the null well look at the p-value
which is labeled as sig significance
point zero zero eight way less than
naught point naught 5 indeed it's even
less than naught point naught 1 so we
conclude there's very strong evidence to
reject the null that the model has no
exponent or power ok next coefficients
this is the the most interesting of all
because it tells us about the
relationship between IVs and the DV for
the coefficients ok so first of all
we'll just look at each each of these
rows here this is a corresponding T
statistic all right we're interested in
the ones for the IVs so experience T
statistic is 2.4 AIDS
significance naught point naught 1/8 now
what is the null for the T step here by
default the null for the t stat in the
regression is that the coefficient for
the IV is 0 that's same as saying that
the IV doesn't help predict the DV that
particular IV all right so this
experience is experience significant yes
we reject the null because the p-value
for this T is 0.01 8 which is less than
0.05 schooling T is 2.9 67 significance
point 0 5 that is less than naught point
naught 5 if you're unsure just get out
you calculate a naught point naught 5
minus not point naught naught 5 is
positive so they are both significant so
so in other words they each have
predictive ability for DV next we move
on to the coefficients go to hell I hate
every time you dock sits always got this
yellow thing box flashing up double
click to activate get rid of that
okay there is again right now where was
I right coefficients where these
coefficients are interesting we're going
to understand the data rather than
standardized coefficients we can either
understand those coefficients these
coefficients we need to check two things
first of all does the sign make sense
as positive or negative contour what
theory suggests in this case education
Theory so experience on on salary well
on earnings will you expect that the
more experience you have the higher
earnings you should get to you would
expect a positive coefficient indeed we
do because it's positive not put
one-eight-five for schooling you expect
the more years of schooling you have the
higher the earnings so that works out to
be positive there you go positive point
two seven six eight next comes on to the
interpretation of the coefficients an
interpretation for experience goes like
well let's um step back a bit in general
the coefficients on the IV in multiple
regression goes like this for a one unit
increase in IV the model predicts that
the DV will increase or decrease
depending on the sign on the coefficient
by blah blah blah units holding all
other IVs constant so I say that again
because as important set in another way
the model predicts that for a one unit
increase in that IV the DV will increase
or decrease by blah-blah-blah units
holding all other IVs fixed let's do
that now for this example so experience
one point eight five four call it
experiences measuring years and earnings
is measuring thousands of dollars so we
would say the model predicts that for a
one year increase
in experienced work experience the
earnings will increase by x is 5000 1854
dollars holding years of schooling fixed
KY said 1854 is because I could have
said it's 1.85 for thousands of dollars
so instead of saying thousands one point
eight four thousand dollars converted
just times that by a thousand okay next
one years schooling coefficient is plus
two point seven six eight we would say
that the model predicts that for an
additional year of schooling the
earnings will increase by two thousand
seven hundred and sixty eight dollars
holding years of experience fixed okay
and that is the interpretation of the
unstandardized coefficients for the
standardized coefficients the which is I
have let me use this but some of you may
need to report it is that everything the
unit's
like when I said one unit increase in IV
leads to a blah blah blah increase or
decrease in the you in in the DV by so
many units the units are our standard
deviations so for experience we would
say that by one standard deviation
increasing experience the motor predicts
that the earnings will increase by 0.35
eight standard deviations alright it
just gives you an idea of the
sensitivity of the DV to changes of the
IV but in terms of real-life
interpretation doesn't talk about stand
deviations doesn't mean much to people
alright so for that reason this is what
we
okay now if I can just review then
quickly all summer we're interested in
reporting the adjusted r-square the
anova were interested in reporting the f
now if it fails the f there is no point
continuing to look at the coefficients
because it fills the f it means that
model is useless okay if it passes the F
we move on to this one and then we look
at the T now if these T's out that's
significant we look at these
coefficients check the sign to the next
sense from a theorist viewpoint if they
don't make central reserve point move
your theory it might mean that you
haven't included you haven't included
something key IVs so you might be
missing some variables all right
if those signs of those coefficients
matches with what you expect from theory
by theory I don't means the discovery I
mean theory of the application of the
data for example here we're looking at
education data source from education
theory if you're doing something from
psychology you'd look at you appeal
psychology Theory from what you expect
the science to be and for economics and
so on so once these signs do make sense
that we can use it for interpretation to
a petition of the coefficients right now
one final thing to say is that and it's
important as well is that these test
statistics the F T only are valid if
certain conditions hold for the model
okay and this is where you do a residual
analysis or what they call diagnostic
checking so in reading off the F and T
I've assumed that certain things about
the model hold and so that these things
are valid okay so that concludes the
very very basic introduction to multiple
regression