Power Curve Fit - HP 12c Platinum Reference Manual

104 Statistics

Power Curve Fit

Another method of analysis is the power curve or geometric curve. The equation of the
power curve is y = Ax
linear regression. Some examples of power curves are shown below.
Y
0
The following keystrokes fit a power curve according to the equation ln y = ln A + B(ln x):
1. Press f CLEAR H .
2. Key in the first y-value and press g° . Key in the first x-value and press
g°_ . Repeat this step for all data pairs.
3. Press gR~ , to obtain the correlation coefficient (between ln y and ln x).
4. Press 0 gRg> to obtain A in the above equation.
5. RPN: Press 1 gR 0 gR~d- to obtain B.
5. ALG: Press 1 gR 0 gR-~d³ to obtain B.
6. To make a y-estimate, key in the x-value and press g°gRg> .
Example: If Galileo had wished to investigate quantitatively the relationship between the
time (t) for a falling object to hit the ground and the height (h) it has fallen, he might have
released a rock from various levels of the Tower of Pisa (which was leaning even then)
and timed its descent by counting his pulse. The following data are measurements Galileo
might have made.
B
, and the values for A and B are computed by calculations similar to
B < 0
X
t (pulses) 2
h (feet) 30
Y
0 < B <1
0
2.5 3.5 4 4.5
50 90 130 150
B > 1
X