Residuals worksheet and predicted values
In the Linear Mixed Effects object, predicted values for the dependent variables are computed at all of the input data points. To obtain predicted values for data points other than the observed values, supply the desired points in the input dataset with missing dependent variables. Predicted values are estimated by using the rows of the fixed effects design matrix X as the L matrices for estimation, and therefore the predicted values for the input data are equal to:
where 
are the final fixed parameters estimates.
If a log-transform is selected, then the predicted values are also transformed. The residuals are then the observed values minus the predicted values, or in the case of transforms, the residuals are the transformed values minus the predicted values. The variance of the prediction is as follows:
The standard errors are the square root of the diagonal of the matrix above. T-type intervals for the predicted values are also computed.
The Lower_CI and Upper_CI are the bounds on the predicted response. The level is selected in the Fixed Effects tab of the Linear Mixed Effects object.