Another Excel worksheet, `BESTFIT.XLS`, allows you to see how a
straight-line trend is fitted to randomly varying measurements of an
underlying trend, and the extent to which the trend line estimated
this way reflects the actual trend.

Load the worksheet and resize the window is necessary so your screen looks like this:

The actual trend in this model is a straight line that runs from zero
to 100 over 100 days. You can introduce random noise into the
measurements from which the trend is calculated by setting `Noise`
to the width of the noise band. If `Noise` is 10, measurements
are randomly displaced ± 5 from the actual trend.

You can also add a sinusoidal variation to the basic straight
line trend, anything ranging from a small amplitude, high frequency,
wiggle to a large secular change that ties the trend line into a
knot. `Amplitude` controls the extent of the deviation from a
straight line; the trend will range from -`Amplitude` to +`Amplitude` around the basic straight trend line. `Period`
controls how rapidly the trend line wiggles from its central value in
terms of days between crest and trough.

The fundamental rising trend, modified by the sinusoidal variation
specified by `Amplitude` and `Period`, is shown as a blue line.
The raw data points that result from displacing values on that curve
based on the setting of `Noise` are plotted as green diamonds.
The straight line trend that best fits the noisy data points shown by
the green dots is plotted as a thick red line. To the extent this
line is representative of the actual trend in blue, the trend fitting
procedure can be trusted. Note, as you experiment with this
worksheet, how long period, high amplitude variation in the basic
trend, equivalent to reversals in an established trend of weight loss
or gain, can spoof the trend line calculation and yield misleading
trend estimates.

By John Walker