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## The Regression

The independent variables (up to 9) and the dependent variable for the fit can be parameters or expressions. Up to fifteen constraints  can be put on the data. You can use symbols to distinguish your data but the regression is done over all points. Figure 8 is a graph of the dependent variable vs the fitted value of the dependent variable.

Figure 8: Multiple linear regression plot

```  Edit,Print,Plot,Regress,...?    R
Dependent variable?             TAUE*1000.
Independent variables?          TE  IP/100.  NE/1E13 ;

Dependent variable?
Independent variables?
Constraints?
Symbols?
Error parameter?
Power fit?
Risk level?
Predict new data points?
ANOVA table to a file?

Set?                            ;
Graph of estimated TAUE vs TAUE RETURN
Display the ANOVA table?        Y```

Figure 9: ANOVA Table

A graph of the estimated dependent variable vs the observed dependent variable is shown. The regression coefficients are shown at the top of the page. If an error parameter is specified, error bars are displayed and the errors are used in the regression. If you want a linear least squares fit  of this result, enter F after the graph has been drawn. See section 2.6 for a table of the options that are available after the graph has been drawn. Note that some of the options for the regression program are set from the PLOT menus. For example, you can use the EXTRAS menu in plot to make a color graph in REGRESS. Following the graph you can optionally display the ANOVA table as shown in Figure 9.

The power fit  equation is , where dv is the dependent variable and iv1, iv2 are independent variables. If any of the variables are zero, that record is skipped.

You can predict new data points from the regression. After selecting the regression variables, use the PR option to turn on the prediction code. Then after you see the ANOVA table, you'll be asked for the new x values. Enter the values and you'll see the statistics associated with the new points. Enter ; to return to the main regression program.

All output in REGRESS is labeled with the database, tables, today's date, a sequence number, and the number of points retrieved.

Next: Joint Confidence Regions Up: Multiple Linear Regression Analysis Previous: Multiple Linear Regression Analysis

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