Step 2: Modeling the Trend :: SAS/QC(R) 13.1 User's Guide

Step 2: Modeling the Trend

The next step is to model the trend as a function of hour. The $\bar{X}$ chart in Figure 17.164 suggests that the mean level of the process (saved as DiameterX in the OUTLIMITS= data set SUBMEANS) grows as the log of HOUR. The following statements fit a simple linear regression model in which DiameterX 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 17.165.

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

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

Figure 17.165: Trend Analysis for Diameter from PROC REG

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 17.165 shows that the fitted equation can be expressed as

${\widehat{\bar{X}}}_ t = 9.99 + 0.14\times \log (t)$

where ${\widehat{\bar{X}}}_ t$ is the fitted subgroup average.[39] A partial listing of the OUT= data set REGDATA created by the REG procedure is shown in Figure 17.166.

Figure 17.166: Partial Listing of the Output Data Set regdata from the REG Procedure

X and s Chart for Diameter

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

^[39]Although this example does not check for the existence of a trend, you should do so by using the hypothesis tests provided by the REG procedure.