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.