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MathGroup Archive 2010

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Prediction Bands and Confidence Intervals

  • To: mathgroup at smc.vnet.net
  • Subject: [mg111248] Prediction Bands and Confidence Intervals
  • From: Steve <s123 at epix.net>
  • Date: Sun, 25 Jul 2010 01:57:55 -0400 (EDT)

Hello,

Does anyone have experience using MeanPredictionBands or
SinglePredictionBands ? There doesn=92t seem to be much documentation
available on this.

I have 18 observations of (x, y) ordered pairs assumed to be taken
from the same population:

{{202, 1}, {265, 2}, {363, 3}, {508, 4}, {571, 5}, {755, 6}, {770, 7},
{818, 8}, {868, 9}, {999, 10}, {1054, 11}, {1068, 12}, {1108, 13},
{1230, 14}, {1268, 15}, {1330, 16}, {1376, 17}, {1447, 18}}

which I have fitted to a power relation y(x)=a*x^^b and thru
regression have found adequate values for the parameters (a =
0.000484391 and b = 1.4465); so far so good.

I=92d like to produce 3 separate plots based on confidence intervals
defined below (I think Mathematica calls them Confidence Bands)

1. The 90% confidence intervals associated with the data variation only
2. The 90% confidence intervals associated with the nonlinear model
fit only and
3. The 90% confidence intervals associated with both the data
variation and the fit

Ideally items 2 and 3 would take the form of upper and lower values on
a and b.

So the 3 individual plots would each contain the raw data points, the
fitted function and the plotted confidence intervals from above.  I
know how to do the plotting and the data fitting it=92s generating the
numeric values for the 3 sets of confidence intervals as a function of
x that is not clear.

Thanks for any ideas.


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