HP 12C#ABA hp 12c_solutions handbook_English_E.pdf - Page 161
Power Curve Fit, Standard Error of the Mean, Mean, Standard Deviation, Standard Error for Grouped Data
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• B = Σ----y----i-l--n----x---i--------1n------Σ----l-n----x----i-Σ----l--n----y--i Σ ( ln xi )2 - 1-n ( Σ ln x)2 • A = 1-n (Σyi - BΣ ln xi ) • = A + B (ln x) Power Curve Fit • y = AxB (A>0) • ln y = ln A + Bln x • (---Σ----l--n---x----i l--n---y----i-)- B n Σ( ln xi ) 2 - (---Σ----l--n---x----i-)--2n • A = exp -Σ----l-n----y---i - BΣ-----l-n----x---i n n • = AxB Standard Error of the Mean • SX = S-----X-n Sy = -S----yn Mean, Standard Deviation, Standard Error for Grouped Data 160
160
•
•
•
=
A
+
B
(ln
x
)
Power Curve Fit
•
y
=
Ax
B
(
A
>0)
•
ln
y
= ln
A
+
B
ln
x
•
•
•
=
Ax
B
Standard Error of the Mean
•
Mean, Standard Deviation, Standard Error for Grouped Data
B
Σ
y
i
x
i
ln
1
n
--
Σ
x
i
Σ
y
i
ln
ln
–
Σ
x
i
ln
(
)
2
1
n
--
Σ
x
ln
(
)
2
–
-------------------------------------------------------
=
A
1
n
--
Σ
y
i
B
Σ
x
i
ln
–
(
)
=
B
Σ
x
i
ln
(
)
Σ
y
i
ln
(
)
n
-------------------------------------
Σ
x
i
ln
(
)
2
Σ
x
i
ln
(
)
2
n
--------------------
–
------------------------------------------------
=
A
Σ
y
i
ln
n
-------------
B
Σ
x
i
ln
n
-------------
–
exp
=
S
X
S
X
n
-------
=
S
y
S
y
n
------
=