       statistics questions

• To: mathgroup at smc.vnet.net
• Subject: [mg61863] statistics questions
• From: Chris Chiasson <chris.chiasson at gmail.com>
• Date: Wed, 2 Nov 2005 04:09:31 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Dear MathGroup,

Questions follow below this setup portion:

According to my limited knowledge of statistics:

Let:
dat = x and y doubles

Assume normally distributed errors.
Assume model for y is f[x].

pseudocode follows

regressionparams=DeleteCases[Variables[f[x]],x]
soln=NonlinearRegress[dat,f[x],x,regressionparams]
v=Length[dat]-Length[regressionparams]
t[v_,ci_]=Quantile[StudentTDistribution[v],1-(1-ci)/2]

ymeanpredictionandcis[x_]=f[x]+{t[v,ci],0,-t[v,ci]}
Sqrt[EstimatedVariance]/.soln

-----------------my questions follow in order of importance-------------

I would assume there is a NonlinearRegress option to directly obtain
the confidence interval/margin of error for the mean response. Does
anyone know what that is?

Why do the Mean and Single PredictionCITable results (use
RegressionReport -> {MeanPredictionCITable, SinglePredictionCITable,
SummaryReport} ) have variable height confidence intervals (easily
seen by subtracting lower from upper)?

Why is the input syntax inconsistent from NonlinearRegress to Regress?
I have also noticed that NonlinearRegress takes the exact same
parameters as FindFit, but they take their last two arguments in
reverse order.

What is the point of NonlinearFit if Mathematica has FindFit?

I have noticed that FindFit and NonlinearRegress both return fits with
significance arithmetic intact, while Regress does not.

Thank you for your time,
--
http://chrischiasson.com/contact/chris_chiasson

```

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