# Best regression using ANOVA technique: trend comparisons in a 3x5 factorial

#### jimhemp

##### New Member
Hello all:

I need help using the ANOVA technique to arrive at an appropriate form of a multiple regression equation between the response (disease severity) and the two factors tested (spring rate) and (summer rate) in an field study. The experimental design is a 3 x 5 factorial arranged as a randomized complete block design with four replications. The first factor is spring rate (SPR): 0, 1.2, and 2.4. The second factor is summer rate (SUM): 0, 0.075, 0.15, 0.3, and 0.6.

I have made trend comparisons between the levels of each factor using single d.f. orthogonal polynomial contrasts in SAS (PROC GLM). I have the following coefficients for the equally spaced levels of the SPR factor:

CONTRAST 'Linear Rate Effect for Spring Topdressing'
SPR -1 0 1;
CONTRAST 'Quadratic Rate Effect for Spring Topdressing'
SPR 1 -2 1;​

and these coefficients for the unequally spaced levels of the SUM factor:

CONTRAST 'Linear Rate Effect for Summer Topdressing'
SUM -3 -2 -1 1 5;
CONTRAST 'Quadratic Rate Effect for Summer Topdressing'
SUM 15.5 1 -9.5 -18.5 11.5;
CONTRAST 'Cubic Rate Effect for Summer Topdressing'
SUM -4.524324 4.0648649 4.9513514 -5.491892 1;
CONTRAST 'Quartic Rate Effect for Summer Topdressing'
SUM 21 -64 56 -14 1;​

However, I do not know how to create contrasts for the SPR x SUM interaction contrasts [e.g., SPR(linear) x SUM(linear), SPR(linear) x SUM(quadratic), SPR(linear) x SUM(cubic), etc].

Is this possible to perform these contrasts in SAS, or do I have to do this by hand? I have found procedures described by Gomez & Gomez (1976) to partition a two-factor interaction SS manually, but I'd rather have SAS do the calculations if possible.

Thanks! Last edited: