Hello everyone,
Just a small query about testing significance of coefficients in a
multiple regression using the sequential sum of squares method.
The usual output for a multiple regression (3 predictors included) looks
like
Analysis of Variance
Source DF SS MS F P
Regression 3 SSR MSR MSR/MSE Value
Residual Error n-3-1 SSE MSE
Total n-1 Syy
Source DF Seq SS
X1 1 A
X2 1 B
X3 1 C
Using the sequentiall sums of squares we can test:
Test 1 Test Statistic: A/MSE
Ho B1=0 vs H1 B1 ne 0 (given nothing [except intercept] fitted)
Test 2 Test Statistic: B/MSE
Ho B2=0 vs H1 B2 ne 0 (given X1 and intercept fitted)
Test 3 Test Statistic: C/MSE
Ho B3=0 vs H1 B3 ne 0 (given X2,X1 and intercept fitted)
The interpretation of a significant test 3 is clear....i.e. we would say
that this gives evidence that X3 contributes significantly to the model
given X1 and X2 [and the intercept]are already in the model....so we are
measuring the contribution of X3 as if it were the last variable in the
model (i.e. given that X1 and X2 [and the intercept] are already in the
model).
However, the interpretation of Test 2 is less clear to me as the test
involves SSR(B2|B1,B0) and MSE (of the *full* model containing X1, X2
*and* X3). How should test 2 be interpreted? Does a significant test 2
simply measure the contribution of X2 given that X1 (and the intercept)
are already in the model? If so, this is a little confusing for me as
the MSE used in the calculation of the statistic is for a model
containing all 3 variables.
Can anyone shed some light?
Many thanks,
Kim
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