[patch #6488] test for QR decomposition in REGRESSION

[Jason H Stover]

Follow-up Comment #2, patch #6488 (project pspp):

Randomly generating the data might work, but then the test won't be a
straightforward diff. If the least squares line passes exactly through the
data, the standard errors of the estimated coefficients will be exactly 0.
This stored standard error will be 0 to machine precision, or close to 0, and
will then be used in the denominator of any test statistics appearing in the
't' and 'F' columns of the output tables. Since these values are close to, but
not exactly 0, and also random, dividing by them will produce random, huge
test statistics which will fail the diff. That's what happened to me when I
ran the randomly-generated data through make check (output below).

The problem is that the true value of the test statistic is infinity. So to
use the randomly-generated data in the test, we either need to:

1. Alter the test so it doesn't just diff the results, but actually compares
the relative errors inside the tables, or

2. Change the code to make REGRESSION report 0.0 and FP_INFINITE for the mean
squared error and test statistics, respectively. I suspect this approach would
cause other, bigger problems elsewhere.

Here is the failed test output:

 11c11
< #        |Regression#     1.01E+010|   2|   5.1E+009|6.1E+032|       
.000#
---
> #        |Regression#     1.06E+010|   2|   5.3E+009|9.8E+031|       
.000#
13c13
< #        |Total     #     1.01E+010|1499|           |        |           
#
---
> #        |Total     #     1.06E+010|1499|           |        |           
#
19,21c19,21
< #        |(Constant)#1.23|       .00| .00|6.18E+012|         .00#
< #        |    v1    #4.56|       .00| .38|2.65E+016|         .00#
< #        |    v2    #7.89|       .00| .00|2.31E+016|         .00#
---
> #        |(Constant)#1.23|       .00| .00|2.48E+012|         .00#
> #        |    v1    #4.56|       .00| .37|1.04E+016|         .00#
> #        |    v2    #7.89|       .00| .00|8.95E+015|         .00#
run program
FAILED
FAIL: tests/command/regression-qr.sh


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