*The Four Types of Estimable Functions* |

## Introduction to Reduction Notation

Reduction notation can be used to represent
differences in Sums of Squares for two models.
The notation denotes the complete
main effects model for effects *A*, *B*, and *C*.
The notation

denotes the difference between the model SS for the complete
main effects model containing *A*, *B*, and *C*
and the model SS for the reduced model containing only *B* and *C*.

In other words, this notation represents
the differences in Model SS produced by

proc glm;
class a b c;
model y=a b c;
run;

and

proc glm;
class b c;
model y=b c;
run;

As another example, consider a regression
equation with four independent variables.
The notation
denotes the differences in Model SS between

and

With PROC REG, this is the difference
in Model SS for the models produced by
model y=x1 x2 x3 x4;

and

model y=x1 x2;

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