Step 2: Modeling the Trend

Graphical Enhancements

Step 2: Modeling the Trend

The next step is to model the trend as a function of hour. The $\bar{X}$ 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	Parameter Estimate	Standard Error	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 ${\hat{\bar{X}}}_t$ 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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