This sample subroutine assumes that the first variable in the observation vector is 

 the dependent variable (0 or 1), the variables 2 through NR are independent variables, 

 and variable (NR + 1) is the weight or blowup factor that describes the number of 

 similar observations represented by the sample observation. 



Program Output 



RISK provides a summary of the input and a description of the regression results. 

 The summary of input begins with a tabulation of control information the user has 

 provided to run the program. Also included are tables of means and standard deviations 

 of all variables in the population. The final portion of this summary of input con- 

 sists of three matrices: a matrix of correlation coefficients, an associated matrix 

 of t statistics indicating the significance of the correlation coefficients, and a 

 product moment matrix. 



The output dealing with regression results may be broken into two sections: (a) A 

 list of the parameter estimates and error mean square resulting from each of the passes 

 through the data followed by the final parameter estimates and (b) the measures of 

 goodness-of -fit . These measures are a table of t statistics, an analysis of variance 

 table, and a table of chi-square statistics. 



The first table of t statistics were calculated on the assumption that error mean 

 square is 1 (i.e., the model provides a perfect fit of the data). The second table is 

 calculated using the actual error mean square provided by the analysis of variance. 

 Neither of these statistics is truly distributed according to the t distribution, 

 because the (X'X) 1 matrix is constructed utilizing estimated values of PQ as weights. 

 The statistics in the first table are approximately normally distributed and the sta- 

 tistics in the second table are approximately distributed according to the t distri- 

 bution. As the error in predicting P becomes negligible, these approximations improve. 



The user may request intermediate output for any pass through the data that 

 includes a matrix correction. This output consists of the (X'X) -1 matrix and the vec- 

 tor of regression coefficients that exist at those points in the pass forwhich inter- 

 mediate output is requested. This same output is provided following the final observa- 

 tion in any pass that included a matrix correction. The (X'X) matrix is also printed 

 at this time. The (X'X)" 1 and (X'X) matrices both before and after correction, the 

 regression coefficients before and after correction, and the regression coefficients 

 that were used to start the pass are printed at the ooint of matrix correction. 



Error Diagnostics 



Six messages are generated by RISK to explain abnormal terminations of the program: 



MORE THAN NC DATA CARDS HAVE BEEN INCLUDED IN THIS RUN 



This diagnostic message is generated when there are more cards in the card input 

 file than are specified, which could occur either from incorrectly counting the number 

 of observations in the input data set or as the result of incorrectly preparing the 

 set of control cards. 



THE NUMBER OF REGRESSORS NR IS IN EXCESS OF THE PRESENT PROGRAM MAXIMUM OF 30 



This diagnostic message is generated if the specified number of regressors, NR, 

 is greater than 30. This check is made before the population of observations is read 

 into the machine; if NR is greater than 30, program execution is terminated. 



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