A residual is the difference between an observed value and a fitted value. This part of the observation is not explained by the fitted model. The residual of an observation is:
When batch is a random factor, Minitab calculates 2 types of residuals. Marginal residuals use the fitted value for a random batch, so the coefficient for batch is not in the equation.
Conditional residuals use the fitted value for a batch that is in the data.
|yi||ith observed response value|
|ith fitted response value|
|the vector of fitted responses|
|X||the design matrix for the fixed effects|
|the vector of fixed predictors|
|Z||the design matrix for the random factors|
|the vector of the estimated BLUP values|