MPO 581 Class number 15/27 Mar 9, 2011
1. Last words on Line fitting by least squares
(applet
from wikipedia page on Least
absolute deviations (LAD) )
Correlation
and
dependence (wikipedia)
Pearson
correlation
More than you wanted to know about line fitting (but only 10 pages)
--
Abstract. The representation of
data, whether geophysical observations, numerical model output or
laboratory results, by a best fit straight line is a routine practice
in the geosciences and other fields. While the literature is full of
detailed analyses of procedures for fitting straight lines to values
with uncertainties, a surprising number of scientists blindly use the
standard least-squares method, such as found on calculators and in
spreadsheet programs, that assumes no uncertainties in the x values.
Here, the available procedures for estimating the best fit straight
line to data, including those applicable to situations for
uncertainties present in both the x and y variables, are reviewed.
Representative methods that are presented in the literature for
bivariate weighted fits are compared using several sample data sets,
and guidance is presented as to when the somewhat more involved
iterative methods are required, or when the standard least-squares pro-
cedure would be expected to be satisfactory. A spreadsheet- based
template is made available that employs one method for bivariate
fitting.
Hsieh Ch. 1-2 -- regression,
correlation, principal components
Open questions, assignments, and
loose
ends for next class:
Testable questions about today's
material:s