Bivariate Statistics - MATLAB Recipes for Earth Sciences - page 120

Fig. 4.1 Display of a bivariate data set. h e thirty data points represent the age of a sediment
(in kiloyears before present) at a certain depth (in meters) below the sediment-water interface.
h e combined distribution of the two variables suggests a linear relationship between age and
depth , i.e., the rate of increase in the sediment age with depth is constant. A Pearson's correlation
coei cient (explained in the text) of r =0.96 supports a strong linear interdependency between
the two variables. Linear regression yields the equation age =21.2+5.4 depth , indicating an
increase in sediment age of 5.4 kyrs per meter of sediment depth (the slope of the regression
line).
regression equation can then be used to calculate the second parameter.
h is chapter i rst introduces correlation coei cients (Section 4.2), and then
explains the widely-used methods of linear and nonlinear regression analysis
(Sections 4.3, 4.9 and 4.10). A selection of other methods that are also used
to assess the uncertainties in regression analysis are also explained (Sections
4.4 to 4.8). All methods are illustrated by means of synthetic examples since
these provide an excellent means of assessing the i nal outcome. We use
the Statistics Toolbox (MathWorks 2014), which contains all the necessary
routines for bivariate analysis.
4.2 Correlation Coei cients
Correlation coei cients are ot en used in the early stages of bivariate
statistics. h ey provide only a very rough estimate of a rectilinear trend in
a bivariate data set. Unfortunately, the literature is full of examples where
the importance of correlation coei cients is overestimated, or where outliers
in the data set lead to an extremely biased estimation of the population
correlation coei cient.