| The TRANSREG Procedure |
| Hypothesis Tests with One-Way ANOVA |
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 90.75:
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;
| Class Level Information | ||
|---|---|---|
| Class | Levels | Values |
| x | 3 | a b c |
| Univariate ANOVA Table Based on the Usual Degrees of Freedom | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares | Mean Square | F Value | Pr > F |
| Model | 2 | 74.00000 | 37.00000 | 37.00 | 0.0004 |
| Error | 6 | 6.00000 | 1.00000 | ||
| Corrected Total | 8 | 80.00000 | |||
| Univariate Regression Table Based on the Usual Degrees of Freedom | |||||||
|---|---|---|---|---|---|---|---|
| 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 |
| Implicit Intercept Model |
| Number of Observations Read | 9 |
|---|---|
| Number of Observations Used | 9 |
| Analysis of Variance | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F |
| Model | 2 | 74.00000 | 37.00000 | 37.00 | 0.0004 |
| Error | 6 | 6.00000 | 1.00000 | ||
| Corrected Total | 8 | 80.00000 | |||
| 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 |
|---|
| Parameter Estimates | ||||||
|---|---|---|---|---|---|---|
| Variable | Label | DF | Parameter Estimate |
Standard Error |
t Value | Pr > |t| |
| Intercept | Intercept | B | 4.00000 | 0.57735 | 6.93 | 0.0004 |
| xa | x a | B | -3.00000 | 0.81650 | -3.67 | 0.0104 |
| xb | x b | B | 4.00000 | 0.81650 | 4.90 | 0.0027 |
| xc | x c | 0 | 0 | . | . | . |
| Implicit Intercept Model |
| Number of Observations Read | 9 |
|---|---|
| Number of Observations Used | 9 |
Copyright © 2009 by SAS Institute Inc., Cary, NC, USA. All rights reserved.