OLS results - Sun ----Number of Digits----- Model Beta SE(B) FStat R**2 Pass=1/Fail=0 Norris11 12.2 14.2 14.1 15.0 1. Pontius 11.9 12.7 12.4 15.0 1. NoInt1 14.7 14.8 0.0* 0.0** 1. NoInt2 15.0 14.9 0.0* 0.0** 1. Filippelli 0.0S 0.0S 0.4 2.7 0. Longley 11.7 12.4 12.4 14.9 1. Wampler1 9.2 15.0 0.0I 15.0 1. Wampler2 12.5 15.0 0.0I 15.0 1. Wampler3 9.0 13.5 13.4 15.0 1. Wampler4 8.9 13.8 15.0 15.0 1. Wampler5 7.3 13.8 13.1 14.2 1. OLS summary: 10./11 passed. Notes: * In the No Intercept regressions, TSP does not report an F-statistic, although one could easily be defined as @COEF'@VCOV"@COEF or @T**2 in these single-regressor models. ** In the No Intercept regressions, TSP defines R**2 differently from NIST. TSP uses the squared correlation between actual and fitted values. NIST apparently uses the formula 1 - @SSR/(y'y) . This formula is not invariant to the mean of y. For example, if there is a single regressor which is nearly constant (but not quite constant), and y has a large mean, this formula will yield a large R**2 value, but a regression on a plain constant will yield R**2 = 0 (with the standard formula), even though the two equations have nearly the same SSR. Controversy in defining R**2 in the no intercept case is nothing new, and it's curious why NIST might be taking a particular stance on this cloudy issue. S In Filippelli, TSP detected singularity, and set the last 2 coefficients and standard errors to zero. It still obtained an approximate fit, judging from the digits in Fstat and R**2. Judging also from the results of other packages, this appears to be a difficult problem with double precision data. I In Wampler1 and Wampler2, there is a perfect fit, so the F-statistic is infinite. Since infinity can't be represented on a computer, it's not clear how to define a number of significant digits for this case.