Sharp PC-1500 Applications Manual page 46

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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', coefficients
a and b, and correlation coefficien t r are determined.
Next, the exponential curve is printed out by the printer, and the input data and
estimated 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 value 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)
F ind the coefficients a and b so that the graph of y=ab" . ..
(I)
is most applicable
to the given number (n) of points (x
1 ,
y
1
) ,
(x
2 ,
y
2 ) •••••
Cxn, y
0 ).
The method of least squares is normally used for the curve application. The
exponential function is, however, difficult to handle, therefore, the conversion is
made by using the logaritlun.
Taking the logarithm of both sides of Eq. (
1)
y=ab' (using natural logarithm)
yields:
2n
y
= £n
a +
x£n b . .... . . . . . . . . . . ....... . . . . . . .. . . . . . . ...... . .
(2)
Now, 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 Bare found , a and bare determined from a =eA and b=eB since A=.Qn a
and B=Qn b.
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