Consider the following missing data problem:
y = c(1, 2, 2, 2, 3)
a = factor(c(1, 1, 1, 2, 2))
b = factor(c(1, 2, 3, 1, 2))
fit = lm(y ~ a + b)
anova(fit)
Analysis of Variance Table
Response: y
Df Sum Sq Mean Sq F value Pr(>F)
a 1 0.83333 0.83333 1.3637e+33 < 2.2e-16 ***
b 2 1.16667 0.58333 9.5461e+32 < 2.2e-16 ***
Residuals 1 0.00000 0.00000
---
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Warning message:
In anova.lm(fit) :
ANOVA F-tests on an essentially perfect fit are unreliable
I am trying to understand how R computes sums of squares. I know that R
makes a FORTRAN call to dqrls to make a QR decomposition of the design
matrix, which returns (among other things),
fit$effects
(Intercept) a2 b2 b3
-4.472136e+00 9.128709e-01 7.715167e-01 7.559289e-01 2.471981e-17
Can anyone elaborate on how R computes these effects? I am not satisfied
with the explanation that R provides with the help(effects) command.
Thanks in advance.
Ethan
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