This example shows how you can use lack-of-fit tests with the REG procedure. See the section Testing for Lack of Fit for details about lack-of-fit tests.
In a study of the percentage of raw material that responds in a reaction, researchers identified the following five factors:
the feed rate of the chemicals (FeedRate), ranging from 10 to 15 liters per minute
the percentage of the catalyst (Catalyst), ranging from 1% to 2%
the agitation rate of the reactor (AgitRate), ranging from 100 to 120 revolutions per minute
the temperature (Temperature), ranging from 140 to 180 degrees Celsius
the concentration (Concentration), ranging from 3% to 6%
The following data set contains the results of an experiment designed to estimate main effects for all factors:
data reaction; input FeedRate Catalyst AgitRate Temperature Concentration ReactionPercentage; datalines; 10.0 1.0 100 140 6.0 37.5 10.0 1.0 120 180 3.0 28.5 10.0 2.0 100 180 3.0 40.4 10.0 2.0 120 140 6.0 48.2 15.0 1.0 100 180 6.0 50.7 15.0 1.0 120 140 3.0 28.9 15.0 2.0 100 140 3.0 43.5 15.0 2.0 120 180 6.0 64.5 12.5 1.5 110 160 4.5 39.0 12.5 1.5 110 160 4.5 40.3 12.5 1.5 110 160 4.5 38.7 12.5 1.5 110 160 4.5 39.7 ;
The first eight runs of this experiment enable orthogonal estimation of the main effects for all factors. The last four comprise four replicates of the centerpoint.
The following statements fit a linear model. Because this experiment includes replications, you can test for lack of fit by using the LACKFIT option in the MODEL statement.
proc reg data=reaction; model ReactionPercentage=FeedRate Catalyst AgitRate Temperature Concentration / lackfit; run;
Output 76.6.1 shows that the lack of fit for the linear model is significant, indicating that a more complex model is required. Models that include interactions should be investigated. In this case, this will require additional experimentation to obtain appropriate data for estimating the effects.
Analysis of Variance | |||||
---|---|---|---|---|---|
Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F |
Model | 5 | 990.27000 | 198.05400 | 33.29 | 0.0003 |
Error | 6 | 35.69917 | 5.94986 | ||
Lack of Fit | 3 | 34.15167 | 11.38389 | 22.07 | 0.0151 |
Pure Error | 3 | 1.54750 | 0.51583 | ||
Corrected Total | 11 | 1025.96917 |
Root MSE | 2.43923 | R-Square | 0.9652 |
---|---|---|---|
Dependent Mean | 41.65833 | Adj R-Sq | 0.9362 |
Coeff Var | 5.85533 |