One-way ANOVA models are fit with either an explicit or implicit intercept. In implicit intercept models, the ANOVA table of PROC TRANSREG is the correct table for a model with an intercept, and the regression table is the correct table for a model that does not have a separate explicit intercept. The PROC TRANSREG implicit intercept ANOVA table matches the PROC REG table when the NOINT a-option is not specified, and the PROC TRANSREG implicit intercept regression table matches the PROC REG table when the NOINT a-option is specified. The following statements illustrate this relationship and produce Figure 104.74:
data oneway; input y x $; datalines; 0 a 1 a 2 a 7 b 8 b 9 b 3 c 4 c 5 c ;
title 'Implicit Intercept Model'; proc transreg ss2 data=oneway short; model identity(y) = class(x / zero=none); output out=oneway2; run; proc reg data=oneway2; model y = xa xb xc; /* Implicit Intercept ANOVA */ model y = xa xb xc / noint; /* Implicit Intercept Regression */ run; quit;
Figure 104.74: Implicit Intercept Model
Univariate Regression Table Based on the Usual Degrees of Freedom | |||||||
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Variable | DF | Coefficient | Type II Sum of Squares |
Mean Square | F Value | Pr > F | Label |
Class.xa | 1 | 1.00000000 | 3.000 | 3.000 | 3.00 | 0.1340 | x a |
Class.xb | 1 | 8.00000000 | 192.000 | 192.000 | 192.00 | <.0001 | x b |
Class.xc | 1 | 4.00000000 | 48.000 | 48.000 | 48.00 | 0.0004 | x c |
Note: | Model is not full rank. Least-squares solutions for the parameters are not unique. Some statistics will be misleading. A reported DF of 0 or B means that the estimate is biased. |
Note: | The following parameters have been set to 0, since the variables are a linear combination of other variables as shown. |
xc = | Intercept - xa - xb |
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