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GB
2.5.5 Exponential regression
The regression formula is y=A e
G
x data the same as that for linear regression.
Estimated values x, and y based on the regression formula can be calculated using the following for-
G
mulas
^
y = A e
Correction is performed the same as in linear regression. Constant term A is obtained
G
by
SHIFT
SHIFT
Σy
and Σxy are obtained by Σlny, Σ(lny)
2
Example
xi
yi
6.9
21.4
12.9
15.7
19.8
12.1
26.7
8.5
35.1
5.2
The data in the above can be
used to obtain the terms of
the regression formula and
the correlation coefficient.
Based on the regression
^
formula, estimated value y
can be obtained for xi=16,
^
and estimated value x can be
obtained for yi=20.
2.5.6 Power regression
The regression formula is y=A.x
G
Estimated values x, and y based on the regression formula can be calculated using the following for-
G
mulas:
^
y = A e
Correction is performed the same as in linear regression. Constant term A is obtained
G
by
SHIFT
EXE
SHIFT
e
x
respectively.
- 36 -
(lny=lnA+Bx). Enter the y date as the logarithm of y(ln), and the
B.x
^
^
Iny - InA
x =
^
Bx
B
, estimated value y is obtained by x
e
x
SHIFT
A
EXE
, and estimated value x is obtained by
Ans
e
x
EXE
and Sx.lny respectively.
2
Key Operation
÷
MODE
SHIFT
Scl
EXE
,
6.9
21.4
In
DT
SHIFT
,
12.9
15.7
SHIFT
In
,
19.8
12.1
In
SHIFT
,
26.7
8.5
SHIFT
In
,
35.1
5.2
SHIFT
In
SHIFT
e
x
SHIFT
A
EXE
SHIFT
B
EXE
SHIFT
R
EXE
16
^
SHIFT
y
EXE
SHIFT
e
x
Ans
EXE
^
20
In
SHIFT
x
EXE
(lny=lnA+Blnx). Enter both data x and y as logarithms (ln).
B
^
^
Iny - InA
^
x =
Bx
, estimated value y is obtained by
e
x
SHIFT
A
EXE
, and estimated value x is obtained by
Ans
e
x
EXE
. Σx
Σy, Σy
and Sxy are obtained by Σlnx, Σ(lnx)
2
2
Ans
EXE
^
^
SHIFT
^
y
in
SHIFT
Display
Remark
Clear memory
6.9
12.9
DT
19.8
DT
26.7
DT
35.1
DT
30.15716545
Constant term A
-0.048870452
Regression coefficient B
-0.997192153
Correlation coefficient r
^
13.79760894
y when xi=16
^
8.403652083
x when yi=20
B
In
y
In
SHIFT
, Σlny, Σ(lny)
2
Copyright L
EXIBOOK
y
^
EXE
. Σy,
x
EXE
x
^
y
SHIFT
x
EXE
and Slnx.lny
2
2002
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