Fitting points with y=t^ p?

Question

Say distance meaurements (y) are performed every second:
t= [0 1 2 3 4 5]

say also that the points (t,y) must be fitted with a graph of the form y=t^p. This is because it is known that there is a power relationship and the disance at zero is zero. It is also known that it is a positive increasing function.

I am given one meausrement and am asked to give an intial guess at what the power function may be.

say at t=3 I am told y = 76,

I would guess p = ln(76)/ln(3) = 3.94
so an equation of y=t^3.94
I give the equation to the person doing the measurements and he saids "thanks the equation fitted the points well"

But say his friend does the same measurements but he measures with another scale, say kilometer instead of meter. So he says at t=3, y= 0.076.

Then I guess the equaiton:
y = t^-2.35

But this guy comes back to be angry and says it looks nothing like the points he measured.

What more do I have to know, or what more should I tell them to improve the fit?

Answer 1

Since you calculated the power based on one data point, this data point simpy has to lie directly on the graph. So I don't see how that person can claim a completely different layout of data points.

Make sure the units part is well understood.

Answer 2

You're predicting a fit from only one data point. The general form of a power curve is
y = ax^b
You need at least two points do determine this equation.

Answer 3

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