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ll
and more
abo
ut Sharp P
C-
1500 at http://www.PC-1500.info
SHARP
PROGRAM
TITLE
EXPONENTIAL REGRESSION AND PLOT
PROGRAM
NO.
PS
- B- 2
I
Outline]
CE- 150 required
With the input data x and y applied
to
the exponential curve y =
a·b',
coefficie
nt
s
a and b, and correlation coefficient r are determined.
Next, the
exponential curve is printed
out
by
the
printer, a
nd
the
input
data and
es
timated values arc plotted.
I Operating Guide ]
(
DEF
! W
[Example
I
x 0.5
Data
input
, printouts
of
coefficients a and b, and correlation co-
efficient r. Up to 39
data
are possible.
Exponential curve
output
and
input
data
arc
plotted on the
graph.
New X
data
are keyed-in and corresponding Y will
be
plotted.
The inputs
of
X are possible up to 39.
For plottable data
of
estimations,
the
estimated y should be
less than
the
maximum
va
lue
of
the
input
data
Y;
.
1.2 3.1
7.4
n = 4
y 7.01 I 1.72 44.54 936.71
Apply
the
above data to y =
ab',
and estimate
the
values when x = 2, 4, 6, and
6.5.
I Contents I (Formulas)
Find the coefficients a and b so
that
t
he
graph
of
y=ab" .
..
(I)
is
most
applicable
to
the given number (n)
of
points
(x
1
,
y
1
) ,
(x
2
,
y
2
)
•••••
Cx
n, y
0
).
Th
e method
of
least squares is normally used for
the
curve application. The
ex
ponential function is, however, difficult
to
handle, therefore, the conversion is
made
by
using
the
logaritlun.
Taking the loga
ri
thm
of
both
sides
of
Eq. ( 1)
y=ab'
(using natural logarithm)
yields:
2n y = £n a + x£n b .
....
. . . . . . . . . .
.......
. . . . . .
..
. . . . . .
......
. .
(2)
N
ow
, assuming Y = 2n y,
A=
2n a, B = 2n b, the following is obtained:
Y
=A+
Bx
.....
.
..
.
...............
. . .
....
.
......
. . .
...
.
.....
(3)
Hence, A and B can be calculated as follows:
A= Y- Bx
B =
~xiYi
-
nxY
'
l:
x
1
i -
-n
xi
(y
l
~
y . y . e . - I ~ .
=
-.£..o
l , l =
nyl
. x
=-
""'
x t
n •·1 n i
...
1
When A and
Ba
re found, a and
bare
determined from a=
eA
and
b=eB
since
A=.Qn
a
and
B
=Qn
b.
Do
not
sale this PDF
!!!
-
40
-
1
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