Fitting nature´s basic functions. II. Estimating uncertainties and testing hypotheses

For pt.I see ibid., previous issue. In the last issue we considered a linear statistical model. The development was motivated by global annual average temperature data which were plotted as discrete circles. The two curves are the best-fitting first- and fifth-degree polynomials. The fifth-degree polynomial tracks the data better, but we need more statistical analysis to determine whether the improvement obtained justifies the addition of four new free parameters. This is one of the questions that we address in this installment. We discuss simple diagnostics for the fit, uncertainties in the estimates, estimate correlations, assigning confidence levels, testing hypotheses, and a time series diagnostic