Three-dimensional scatterplot of data

Data from a randomised block experiment can be displayed in a three-dimensional scatterplot:

Model

Both blocks and treatments explain some variability in the response measurement, Y, but...

Blocks and treatments are modelled in the same way:

y = (overall mean) + (effect depending on block)
         + (effect depending on treatment) + error

The error is again assumed to have a normal distribution with mean zero and constant standard deviation. Within any block, changing the treatment simply adds or subtracts a constant to the response.