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matteo_patelmo

Community Trekker

Joined:

Dec 23, 2015

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?

 

thanks  a lot in advance.

Matteo