Page 90 - MATLAB Recipes for Earth Sciences
P. 90

82                                                  4 Bivariate Statistics

                                      Curvilinear Regression
                800

                700
                600
                                                     i-th data point
                500
               Barium content (%)  400  95% Confidence Bounds


                300
                200

                100
                                                        95% Confidence Bounds
                  0
                                         Regression line
               ï100

               ï200
                   0     2     4    6     8    10   12    14    16   18    20
                                      Depth in sediment (meters)
            Fig. 4.8 Curvilinear regression from barium contents. The plot shows the original data points
            (plus signs), the regression line for a polynomial of degree n=2 (solid line) as well as the error
            bounds (dashed lines) of the regression.




            The plot nicely shows that the quadratic model for this data is a good one.
            The quality of the result could again be tested by exploring the residuals,
            employing resampling schemes or cross validation. The combination of re-
            gression analysis with one of these methods represent a powerful tool in
            bivariate data analysis, whereas Pearson·s correlation coeffi cient should be
            used only as a first test for linear relationships.



            Recommended Reading

            Alberède F (2002) Introduction to Geochemical Modeling. Cambridge University Press
            Davis JC (2002) Statistics and data analysis in geology, third edition. John Wiley and Sons,
               New York
            Draper NR, Smith, H (1998) Applied Regression Analysis. Wiley Series in Probability and
               Statistics, John Wiley & Son
            Efron B (1982)  The jackknife, the bootstrap, and other resampling plans. Society of
   85   86   87   88   89   90   91   92   93   94   95