Understanding multicollinearity between the solar coefficient and linear trend coefficient in ordinary least squares regression.

Salt Lake City Community College

When doing regression multicollinearity between model variables can be a problem. This is a problem for time and solar coefficients for data sets of mesospheric temperatures spanning one solar cycle or less. This paper focuses on the problem of multicollinearity between the linear term and the solar term in an ordinary least squares regression (OLSR). The multicollinearity between those two terms will change according to the phase of the solar cycle. If solar maximum occurs in the middle of the second half of the data set there is significant negative correlation between them. Conversely, if solar maximum occurs in the middle of the first half of the data set there is significant positive correlation. The optimal phase of the solar cycle relative to the data is for solar max or solar min to occur in the time center of the data set. In that particular case the correlation between the linear and solar coefficients is minimized. When the data set spans approximately 1.3 solar cycles or greater then multicollinearity between the time coefficient and solar coefficient is not an issue. The degree of multicollinearity is independent of the magnitude of the solar response and cooling rate.