Calculate Prediction Interval for Regression by hand...

Hi again,

thank you all for you tips with predict, predict.lm etc.
From summary(lm-model), I can get the Estimate and the Standard
Error for intercept and slopes. With confint I can get confidence
intervals (?) for these parameters for different levels.

I want to calculate it by hand, rather then by using R's predict
function, due to some reasons:

1) I want to get the mathematical background
2) I want to use it in a model outside of grass (python-model, and
I don't want to use a direct interaction python-R)
3) I want to calculate it with simple programming languages (e.g. simplest form of basic etc.)

In wikipedia it says that it is possible to calculate the prediction interval from the standard error of the parameters. So how is that done exactly? Can anyone guide me to the formula? Or is it just 

Y=b+Intercept + (a1+SE(a1))*X1+(a2+SE(a2)*X2 (of course with all variations in plus and minus SE)?

Your help is greatly appreciated!

/johannes

-------- Original-Nachricht --------
Datum: Mon, 17 Oct 2011 10:36:35 +1100
Von: Chris Howden <chris at trickysolutions.com.au>
An: Johannes Radinger <jradinger at gmx.at>, r-sig-ecology at r-project.org
Betreff: RE: [R-sig-eco] Calculate Prediction Interval for Regression by hand...
Hi Johannes,

predict() will give u SE's and confidence intervals.

U can either use the original data as an input and get a prediction for
all the original data points. Or create an input data set and get
predictions for them.

If your doing an ANOVA type analysis with discrete factors I often use
expand.grid to quickly get a matrix for all combinations. So something
like this
(predict.ci <- data.frame(expand.grid(model$xlevels), predict(model,
expand.grid(model$xlevels), interval="conf")))

There's also confint() which is for single parameters.

Chris Howden B.Sc. (Hons) GStat.
Founding Partner
Evidence Based Strategic Development, IP Commercialisation and Innovation,
Data Analysis, Modelling and Training
(mobile) 0410 689 945
(fax) +612 4782 9023
chris at trickysolutions.com.au

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-----Original Message-----
From: r-sig-ecology-bounces at r-project.org
[mailto:r-sig-ecology-bounces at r-project.org] On Behalf Of Johannes
Radinger
Sent: Sunday, 16 October 2011 10:45 PM
To: r-sig-ecology at r-project.org
Subject: [R-sig-eco] Calculate Prediction Interval for Regression by
hand...

Hi UseRs,

I calculated with lm(Y~X1+X2) successfully a linear regression.
Based on this linear regression with multiple independent variables
I'd like to calculate manually prediction intervals. Therefore I have a
few
questions:

1) I want a prediction interval for Y (like Y+-PI) for a given value
for X1 and X2.
2) I want to calculate the predicition intervall for Y by hand (either
with the mathematical functions of R or with python etc.

So I think I have to extract the prediction interval for the single
regression parameters (intercept and slopes) from the lm model.

I tried to google for a simple solution but wasn't succesfully yet.
I think following link: Prediction interval in Regression analysis
explains very well
what I want to do.

There it says: "...one may use the standard error of the estimates for the
intercept and slope ( and ) to compute a prediction interval". So is that
the right approach?
If yes how can I get the standard error for a and b and which formula
has to used for the calculation?

Thank you very much in advance

Have a nice sunday!

cheers
Johannes

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Calculate Prediction Interval for Regression by hand...

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