The Effects of Model Misspecification on Linear Regression Coefficients as Applicable to Solar and Linear Terms

Salt Lake Community College Student Center

Determining atmospheric solar response from data is typically done by fitting a linear model to the data using a least squares approximation. These models typically include a solar proxy that follows the 11 year solar intensity variation, as well as a linear cooling trend. In this paper it is argued that such a regression model is flawed in that the atmospheric solar response might be out of phase with the solar input. And if so, the phase difference between solar input and atmospheric solar response can significantly bias the linear regression coefficient and attenuate the solar coefficient. This result is important because the sign of the solar response has been noted to change with altitude. Consequently, at some point between these two regions the solar response must go through zero, regardless of whether the actual solar response is zero at that altitude.