Fwd: MINITAB DEMO Notes Doubts

[Shachit Iyer]

---------- Forwarded message ----------
From: Kannan A <kan...@iitm.ac.in>
Date: Tue, Nov 6, 2012 at 8:47 PM
Subject: RE: MINITAB DEMO Notes Doubts
To: Aswathy Surendran <aswathy....@gmail.com>
Cc: Shachit Iyer <shach...@gmail.com>, Kannan A <kan...@iitm.ac.in>

 

(1) In slide 48, you are finding Fo value = 61.62. Could you please explain how you arrive at that( because this value is not found in any of the ANOVA calculations you have given)? I mean, what all are the terms that you have considered for obtaining it. Also, is this for the lazy design /reduced design/ actual design.

 

Please see slide 32 (Combined main effects, full model)

 

(2) What are the degrees of freedom for the Model, LOF and Pure Error? For Model is it the #no: of parameters 'p' ?

 

 

Model DOF = all main factors and interactions considered (this does not include the model constant) = 7 for etching problem 2^3 design (A, B, C, AB, BC, AC, ABC)

 

Pure Error   = (number of repeat observations per level setting - 1)*levels of factor A * levels of factor B * levels of factor C = (2-1)*2*2*2 = 8  This is completely independent entity.

 

Total Sum of Squares  (DOF) = Effects or Model Sum of Squares (DOF) + Residual Sum of Squares (DOF) By Definition

 

N  -  1  = 15 )  =    7 (= p-1)  +  (residual SS of squares DOF)

 

( where N is total number of observations = 16, p is the total number of model parameters = 8, constant, A, B, C, AB, BC, AC, ABC (=1+7=8)

 

Effects Sum of Squares  is same as  Model Sum of Squares and is used interchangably here. 

 

 

Residual Sum of Squares (DOF) = TSS (DOF) - Effects or Model Sum of Squares (DOF)

 

                                                  =  N-1            - (p-1) = N-p = 16 - 1 - (8-1) = 15-7=8

 

Pure Error sum of Squares is independent, depends on number of repeats and calculated independently (from center point repeats or level repeats)

 

Residual Sum of Squares is variable and depends upon p the number of parameters used in the model

 

So N-p increases when parameters used in model is less (truncated or lazy model) and gets bloated due to lack of fit terms (due to unused model effects Sum of Squares coming into Residual Sum of Squares Contribution)

 

The difference between Residual sum of squares and error sum of squares degrees of freedom is zero for full saturated model.

 

 

The difference between Residual sum of squares and error sum of squares degrees of freedom is > 0 for unsaturated (truncated/lazy) models.

 

The non zero difference exhibits as LOF dof in unsaturated models.

 

 

 

Please refer to slide 35 also for Design expert output When LOF is not considered then residual error is only considered. 

 

(3) Sir, I have asked in class about R-sqr-adjusted and R-sqr (Slide 49). Which error do I use? You answered then that I should use Residual Error. But in the calculation given, you have used Pure Error. Could you please clarify? 

 

For the example given pure error  = residual error as the full model is used in this case.

 

I am sending this email copy to all students in case they had similar doubts.  Let me know if the above answered your questions.

 

 

Please stick to uniform PPT format for assignment submissions and excel outputs can be cut and pasted to ppt.  This will help the TAS correcting your paper.  Do NOT convert to pdf. 

 

 

 

--
Aswathy Surendran,
Ph.D. Scholar,
Dept. of Aerospace Engg.,
IIT Madras,
Chennai - 600036,
India

--

Shachit Iyer

3rd Year 

Chemical Engineering Dual Degree (B.Tech & M.Tech)
Ganga Hostel

Indian Institute of Technology

Madras
Chennai 36