Least-squares using successive rows – HP 15c User Manual
Page 118
118
Section 4: Using Matrix Operations
118
lÁ
6.963636364
b
1
estimate.
´U
6.963636364
Deactivates User mode.
´•4
6.9636
The Reg SS for the PPI variable adjusted for the constant term is
(Reg SS for reduced model) − (Reg SS for constant) = 51.29864900.
The Reg SS for the UR variable adjusted for the PPI variable and the constant term is
(Reg SS for full model) – (Reg SS for reduced model) = 3.274630500.
Now construct the following ANOVA table:
Source
Degrees of
Freedom
Sum of
Squares
Mean Square
F Ratio
UR | PPI, Constant
1
3.2746305
3.2746305
1.939
PPI | Constant
1
51.2986490
51.2986490
30.37
Constant
1
533.4145457
533.4145457
315.8
Residual (full model)
8
13.5121750
1.68902188
Total
11
601.5000002
The F ratio for the unemployment rate, adjusted for the producer price index change and the
constant is not statistically significant at the 10-percent significance level (α = 0.1). Including
the unemployment rate in the model does not significantly improve the CPI fit.
However, the F ratio for the producer price index adjusted for the constant is significant at
the 0.1 percent level (α = 0.001). Including the PPI in the model does improve the CPI fit.
Least-Squares Using Successive Rows
This program uses orthogonal factorization to solve the least-squares problem. That is, it
finds the parameters b
1
, …, b
p
that minimize the sum of squares
)
(
)
(
||
||
2
Xb
y
Xb
y
r
T
F
given
the model data
n
np
n
n
p
p
y
y
y
x
x
x
x
x
x
x
x
x
2
1
2
1
2
22
21
1
12
11
and
y
X
.
The program does this for successively increasing values of n, although the solution b = b
(n)
is meaningful only when n ≥ p.
It is possible to factor the augmented n × (p + 1) matrix [X y] into Q
T
V, where Q is an
orthogonal matrix,