Methods and formulas for goodness-of-fit statistics in Analyze Factorial Design

S

Notation

TermDescription
MSEmean square error

R-sq

R2 is also known as the coefficient of determination.

Formula

Notation

TermDescription
yi i th observed response value
mean response
i th fitted response

R-sq (adj)

While the calculations for adjusted R2 can produce negative values, Minitab displays zero for these cases.

Notation

TermDescription
ith observed response value
ith fitted response
mean response
nnumber of observations
pnumber of terms in the model

R-sq (pred)

While the calculations for R2(pred) can produce negative values, Minitab displays zero for these cases.

Notation

TermDescription
yi i th observed response value
mean response
n number of observations
ei i th residual
hi i th diagonal element of X(X'X)–1X'
X design matrix

PRESS

Assesses your model's predictive ability and is calculated as:

Notation

TermDescription
nnumber of observations
eiith residual
hi

ith diagonal element of

X (X' X)-1X'

R-sq (WP)

In split-plot designs, R2 (WP) is the proportion of variation among whole plots that is accounted for by all of the terms in the model that involve only hard-to-change factors.

Notation

TermDescription
SS (WPerror)Sum of squares for the whole plot error term
SS Total (WP)Sum of sequential SS for all terms that involve the whole plot error term and only hard-to-change factors

R-sq(SP)

In split-plot designs, R2 (SP) is the proportion of variation among subplots (within whole plots) that is accounted for by the model.

Notation

TermDescription
SS (SPerror)sums of squares for the subplot error term
SS Total (SP)SS Total – SS Total(WP)
SS Total (WP)sum of sequential SS for all terms that involve the whole plot error term and only hard-to-change factors
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