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Community Trekker

## stderr in least square vs generalized regression

Hello, I was analyzing this simple DOE:

A B Y
33 180 3317
33 180 3653
17 230 6133
17 230 6436
25 205 5939
33 230 12431
17 180 1710
17 180 1806
25 205 5578
33 230 13680

with Standard Least Square and with GenReg.

I noticed that while the estimates are exactly the same, GenReg yields smaller stderr (in italics).

Standard Least Square:

Intercept -29469.6125 1390.0621826 -21.20 <.0001
A 265.5625 19.698753398 13.48 <.0001
B 140.97 6.3036010872 22.36 <.0001
(A-25)*(B-205) 6.305 0.7879501359 8.00 0.0002

GenReg (normal, forward selection, min AICc)

Term Estimate Std Error Wald ChiSquare Prob > ChiSquare Lower 95% Upper 95%
Intercept -29469.6125 1210.3742588 592.80177141 <.0001 -31841.90246 -27097.32254
A 265.5625 15.108244044 308.96231754 <.0001 235.9508858 295.1741142
B 140.97 4.834638094 850.20853436 <.0001 131.49428346 150.44571654
(A-25)*(B-205) 6.305 0.6043297618 108.84844181 <.0001 5.1205354322 7.4894645678

Can anyone explain why this is so?

Matteo

1 ACCEPTED SOLUTION

Accepted Solutions
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Staff

## Re: stderr in least square vs generalized regression

I don't see a difference in AICc or BIC between the two platforms, but I definitely see the difference in the standard errors.

In the GenReg platform, if you switch the estimation to Standard Least Squares you will get exactly the same standard errors. You start seeing the differences when that is changed to Stepwise, even though the model is the same.

The answer is due to a different method being used to estimate the standard errors. From the JMP help, Gen Reg is doing this:

Standard Least Squares has a more direct calculation of the standard error.

Dan Obermiller
2 REPLIES 2
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Senior Member

## Re: stderr in least square vs generalized regression

Hi Matteo, I have the same question. Curious as to why RMSE and AICc / BIC differ between the platforms but parameter estimates are the same!
Highlighted
Staff

## Re: stderr in least square vs generalized regression

I don't see a difference in AICc or BIC between the two platforms, but I definitely see the difference in the standard errors.

In the GenReg platform, if you switch the estimation to Standard Least Squares you will get exactly the same standard errors. You start seeing the differences when that is changed to Stepwise, even though the model is the same.

The answer is due to a different method being used to estimate the standard errors. From the JMP help, Gen Reg is doing this:

Standard Least Squares has a more direct calculation of the standard error.

Dan Obermiller