Regression: Partial F-test on a factor coded as a set of dummies - R; SPSS; and by hand Video Lecture | SPSS: For Beginners - Data & Analytics

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in this example I regret on X and a
factor color that can be read Lew green
you can see from the model I have
dummies for blue and green if I want to
test whether the factor color is
significant I need to test that both
parameters on the dummies is zero I can
do this with the partial F test note
this test is not the same as doing T
tests on each of the dummy coefficients
no also there are many of the tests
called the F test so be clear what the
test is doing to do the test will have
to run two models one is to regress Y on
all the regressors this is called the
unrestricted or full model and regress Y
on the same regressors but leaving out
the ones whose parameters are being
tested to be zero this is called the
reduced or restricted model test
statistic may be expressed in terms of
residual sum of squares RSS or in terms
of r-squared from the two models in
either case the key part of the test is
the numerator that computes the
difference in the bit suppose the null
hypothesis is true that the coefficients
are 0 then the RSS and a square and both
models will be similar and so the
difference in our SS and the R square
will be close to 0 and so the F step
will be close to 0 there's a test
statistic value far from 0 points to
rejecting the null formally we compare
the F step to the critical values from
the F table where the degree of freedom
is Q the number of parameters being
tested to be 0 and the other degree of
freedom is n minus P where P stands for
the number of parameters in the full
model including the intercept note the F
star can't be negative so if you get a
negative number it means you probably
got the differences the wrong way around
the apostle f statistic is derived
supposing the assumptions of classical
linear regression hold so we should
check these conditions before running
the test I won't be doing this in the
example that I want to focus on doing
the test so we'll suppose all the
conditions are met SPSS does not
actually do the test automatically so we
have to do it by hand
some of you may need to do it anyway for
the exam by hand his output from SPSS to
get RSS and the sample size I'll show
you how to get these tables at the end
of the video is the calculation based on
RSS the stat comes to just over 22 and
exceeds the critical value at the 5%
level and indeed even at the 1
significance level so we conclude there
is very strong evidence to reject the
null that the factor is not significant
ie
is evidence to retain it no they've
degrees of freedom on earth table to
find critical value so to here
corresponds the number of parameters
being tested and 146 is the number of
observations minus the number of
parameters in the phone mod will include
an intercept this is 150 minus 4 here's
the test computer using R square the
test statistic value is slightly
different due to rounding and nothing to
worry about the conclusion is the same
our users have an easier time here's the
code to do it in our run both full and
reduced models then use the command and
over to run the partial F test command
as dot factor tells our the variable
color is a factor and I will
automatically create the dummies and
like in SPSS p-value for the test is 3
times 10 to the minus 9 which is less
than naught point naught 1 so we have
very strong evidence against the null
yep the analysis in R is a lot faster
finally let me show you how to run the
two models in SPSS we can run it one by
one but we can run it as blocks that I'm
going to show you how now first go to
analyze regression linear first we want
to run the reduced model so put the wine
V deep in box and X in the independent
instead of clicking on OK we click on
next
250 full model and the full model is x
including the dummies blue and green for
the color I can toggle back and forth
between the two models so we would call
this block 2 I can go back to the model
1 which is called block 1 and when I'm
done I click OK all right so this
produces 2 models model 1 what caused
model 1 is the reduced model and model 2
is the full model and this is for this
ANOVA table the are assessing what one
is there and the total grief in 1.9 and
for model 2 formal RSS's here and the
degree of room is the same
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