Geoscience Reference
In-Depth Information
Fig. 4.9
Comparison of unweighted (dashed line) and weighted (solid line) regression result
from synthetic data. h e plot shows the original data points (circles), the error bars for all
data points, and the regression line for an exponential model function. In the unweighted
regression, the i tted curved is moved towards the i rst two data points (
x
=-0.24823 and
x
=0.60753) with a large error, while in the weighted regression it is moved towards the third
data point (
x
=0.73846) with a small error.
Comparing the coei cients
p
and the red curves from the weighted regression
with the previous results from the unweighted regression reveals slightly
dif erent results (Fig. 4.9):
errorbar(data(:,1),data(:,2),data(:,3),'o')
hold on
plot(data(:,1),fittedcurve_1,'r--')
plot(data(:,1),fittedcurve_2,'r-')
xlabel('x-Axis'), ylabel('y-Axis')
title('Comparison of Unweighted and Weighted Fit')
hold off
As an example, in the unweighted regression the i tted curved is moved
towards the i rst two data points (
x
=0.24823 and
x
=0.60753) with a large
error, while in the weighted experiment it is moved towards the third data
point (
x
=0.73846) with a small error.
Recommended Reading
Albarède F (2002) Introduction to Geochemical Modeling. Cambridge University Press,
Cambridge
Davis JC (2002) Statistics and Data Analysis in Geology, h ird Edition. John Wiley and Sons,
New York
