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## Joint Confidence Regions

Figure 10: Joint confidence region

You can study joint confidence regions [8]. This option will display a table of regression fit coefficients and their independent standard errors followed by a plot composed of many points as shown in Figure 10.

```    Joint confidence region study?  Y

\* Options are:
1) Write coefficients to a file?
2) Number of Monte-Carlo hits (default is 1000)?
3) Standard deviation half-length (default is 3.)?

<7=J;> JCR options? <W>:        ;
Joint confidence region plot    RETURN```

The points overlap to form an elliptical region. This region is the projection into 2d space of the joint confidence region for all the variables considered together, not independently. When you give a risk level  (default is 0.05), you determine a confidence level , 1 - risk level, which is used in the ANOVA  table to determine the upper and lower confidence limits for each regression coefficient independently. This same confidence level is used in the joint confidence region, i.e. for risk level of 0.05, you have 95% confidence that the fit coefficients will end up in the n-d ellipsoid which is projected onto the 2d plane of the graph. The two dimensions of the plot are the regression coefficients for the first two variables you specified in the regression fit.

What does it mean to say ``you have 95% confidence that...''? It means that, based on the scatter of the data around the fit line, if you rescattered the data again around the fit line by that much, you would get fit coefficients within the ellipsoid 95% of the time.[9]

Marilee Thompson
Fri Jul 11 17:05:56 EDT 1997