HP HP-15C Advanced Functions Handbook

1 32 Section 4: Using Matrix Operations
• E(r) = 0, where r = y — Xb is the vector of residuals.
• E(||y - Xb||f.) = (71 - p)a2, so that a2 = ||r|||/(7i - p) is an
unbiased estimator for a2. You can estimate Cov(b) by
replacing o2 by a2.
The total sum of squares \\y\\p can be partitioned according to
II 119 T
\\y\\F = y y
= (y - Xb + Xb)r(y - Xb + Xb)
= (y - Xb)T(y - Xb) ~ 2bTXr(y - Xb) + (Xb)T(Xb)
/ Residual \ Regression \m of Squares/ \Surn of Squares/
When the model is correct,
and
for b T^ 0. When the simpler model y — r is correct, both of these
expectations equal a2.
You can test the hypothesis that the simpler model is correct
(against the alternative that the original model is correct) by
calculating the F ratio
r — •
F will tend to be larger when the original model is true (b ^ 0) than
when the simpler model is true (b = 0). You reject the hypothesis
when F is sufficiently large.
If the random errors have a normal distribution, the F ratio has a
central F distribution with p and (n — p) degrees of freedom if
b = 0, and a noncentral distribution if b ^ 0. A statistical test of the
hypothesis (with probability a of incorrectly rejecting the
hypothesis) is to reject the hypothesis if the F ratio is larger than
the lOOa percentile of the central F distribution with p and (n — p)

HP HP-15C Specifications

General

Brand	HP
Model	HP-15C
Category	Calculator
Language	English