Fitting Nature's Basic Functions Part II. Estimating Uncertainties and Testing Hypotheses
Bert W. Rust
This paper is the second in a series on fitting combinations of basic mathematical functions to measured data from the real world. This installment explains statistical diagnostic techniques for evaluating linear least squares fits. Topics covered include the variance and correlation matrices for the least squares estimate, construction of confidence intervals for the estimate, and testing hypotheses about the statistical significance of the individual components of the estimate. The use of the techniques is illustrated by applying them to the analysis of polynomial fits to the measured global average annual temperature record for the years 1865-1999.
global temperature, linear estimation, linear least squares, linear regression
Fitting Nature's Basic Functions Part II. Estimating Uncertainties and Testing Hypotheses, Computing in Science & Engineering, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=150837
(Accessed March 2, 2024)