Test for harmful collinearity among predictor variables used in modeling global temperature

Lower tropospheric temperature anomalies from the global satellite MSU that have been available since 1979 are unique and play a significant role in the continuing climate debate. A number of investigators have analyzed the MSU data using regression analysis to remove the geophysical effects of volcanoes, El Niño/Southern Oscillation, and solar irradiance in an effort to determine any underlying trend line. In a recent paper Santer et al. (2001; J Geophys Res 106:28033– 28059) questioned the validity of such studies, noting that large El Niño events have occurred at the same time as 2 major volcanoes. They calculated a correlation between these 2 variables and claimed that this indicates collinearity, which can adversely affect any regression analyses. We examine the issue of collinearity between the volcano and El Niño/Southern Oscillation signals in the analysis of the MSU data. We do this by using the general tests for collinearity of Belsley. There are 2 tests. The first is for degrading collinearity on the data matrix of the predictor variables. If the first test fails, a second test for harmful collinearity is performed on the coefficients from any regression analysis. Employing these 2 tests, we find that there is no degrading or harmful collinearity used in the modeling of the MSU temperature anomalies.