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Understanding Basic Statistics • Fitting • Exercise • Excel • Igor • Kaleidagraph • Origin • Power Laws • Dimensional Analysis
When one quantity (say *y*) depends on another (say *x*) raised
to some power, we say that *y* is described by a **power law**. For
example, the distance traveled by an object in free fall (in the absence
of air resistance) is given by

Ignoring the dependence on *g*, this equation says that *s* is
proportional to the square of *t*. Plotting on linear (Cartesian)
axes produces a parabola. Now, a parabola is a very beautiful curve, but
it is difficult to eyeball a curve and say with confidence that it is
a parabola. It is even harder to eyeball some data points, with their
uncertainties, and tell whether they follow a parabolic curve.
Eyeballs are much happier with straight lines.

There is a handy way to convert this power-law relationship into a straight
line; just take the logarithm of both sides of the equation:

If we plot log(*s*) on the *y* axis and log(*t*) on the
*x* axis, we get a straight line with slope 2 (which is the exponent
of *t*). Using Kaleidagraph or Origin you can just double-click
the axes to convert the display from linear to logarithmic. You can also
perform a proper c^{2} fit, as described on the Fitting page.

Understanding Basic Statistics •
Fitting •
Exercise •
Excel •
Igor •
Kaleidagraph •
Origin •
Power Laws •
Dimensional Analysis

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