Methods and formulas for goodness-of-fit statistics in Analyze Variability

Notation

R² is also known as the coefficient of determination.

Formula

Notation

Term	Description
yi	i th observed response value
	mean response
	i th fitted response

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

Notation

Term	Description
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

Assesses your model's predictive ability.

Formula

Notation

The calculation of the log-likelihood depends on the estimation method for the analysis.

Least squares estimation

Minitab uses the following equation for the log-likelihood:

The weights for the analysis are either the specified weights or given by the following equation:

Maximum likelihood estimation

This calculation of the log-likelihood assumes that the standard deviations are from normal distributions and that the natural log of the standard deviation follows a linear model.

Notation

Term	Description
n	the number of rows with no missing data
R	the sum of squares for error for the model
	the trigamma function
vi	the degrees of freedom for the ith standard deviation
	the gamma function
Si	the ith sample standard deviation
	the row of the design matrix associated with the ith standard deviation
	the maximum likelihood estimates of the model coefficients

AICc is not calculated when .

Notation

Notation

Notation