Confidence interval

Question

With
data = {{0.002, 2.51053}, {0.004, 2.54217}, {0.006, 2.55543}, {0.008, 2.54247}};

I obtain a linear fit 2.51038 + 5.454 x; now I want to get the 95% confidence interval from linear regressions. when I do it with Mathematica, it gives me a pair of data set for the CI. I want to add the CI to x -> 0.000717263, but I don't know how to interpret that.

corey979 · Answer

Is this what you want?
data = {{0.002, 2.51053}, {0.004, 2.54217}, {0.006, 2.55543}, {0.008, 2.54247}};

lm = NonlinearModelFit[data, a x + b, {a, b}, x]

bands[x_] = lm["MeanPredictionBands", ConfidenceLevel -> .95]

Show[ListPlot[data], 
 Plot[{lm[x], bands[x]}, {x, 0, 0.01}, Filling -> {2 -> {1}}], 
 Frame -> True, Axes -> False, PlotRange -> All]

bands[0.000717263]

{2.44077, 2.58781}

Confidence interval

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