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 Graphical Enhancements

## Step 2: Modeling the Trend

The next step is to model the trend as a function of hour. The chart in Figure 47.23 suggests that the mean level of the process (saved as DIAMTERX in the OUTLIMITS= data set SUBMEANS) grows as the log of HOUR. The following statements fit a simple linear regression model in which DIAMTERX is the response variable and LOGHOUR (the log transformation of HOUR) is the predictor variable. Part of the printed output produced by PROC REG is shown in Figure 47.24.

   data submeans;
set submeans;
loghour=log(hour);

proc reg data=submeans ;
model diamterx=loghour;
output out=regdata predicted=fitted ;

proc print data=regdata noobs;
run;


 X and s Chart for Diameter

 The REG Procedure Model: MODEL1 Dependent Variable: diameterX Mean of diameter

 Parameter Estimates Variable Label DF ParameterEstimate StandardError t Value Pr > |t| Intercept Intercept 1 9.99056 0.02185 457.29 <.0001 loghour 1 0.13690 0.00967 14.16 <.0001
Figure 47.24: Trend Analysis for DIAMETER from PROC REG

Figure 47.24 shows that the fitted equation can be expressed as




where is the fitted subgroup average.* A listing of the OUT= data set REGDATA created by the REG procedure is shown in Figure 47.25.

 hour diameterX diameterS diameterN loghour fitted 1 9.9992 0.09726 8 0.00000 9.9906 2 10.1060 0.07290 8 0.69315 10.0855 3 10.1428 0.06601 8 1.09861 10.1410 4 10.1565 0.08141 8 1.38629 10.1803 5 10.1583 0.15454 8 1.60944 10.2109 6 10.2390 0.05095 8 1.79176 10.2359 7 10.2684 0.09619 8 1.94591 10.2570 8 10.2916 0.07510 8 2.07944 10.2752 9 10.2655 0.07053 8 2.19722 10.2914 10 10.3504 0.12049 8 2.30259 10.3058 11 10.3406 0.12849 8 2.39790 10.3188 12 10.2865 0.05592 8 2.48491 10.3307 13 10.2720 0.07849 8 2.56495 10.3417 14 10.4225 0.12093 8 2.63906 10.3518 15 10.4006 0.06253 8 2.70805 10.3613 16 10.3554 0.11340 8 2.77259 10.3701 17 10.3827 0.08683 8 2.83321 10.3784 18 10.3763 0.09874 8 2.89037 10.3863 19 10.3976 0.11531 8 2.94444 10.3937 20 10.3950 0.09185 8 2.99573 10.4007
Figure 47.25: Listing of the Output Data Set REGDATA from the REG Procedure

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