Geoscience Reference
In-Depth Information
clear
agedepth = load('agedepth_1.txt');
meters = agedepth(:,1);
age = agedepth(:,2);
corrcoef(meters,age)
ans =
1.0000 0.9563
0.9563 1.0000
rng(0)
rhos1000 = bootstrp(1000,'corrcoef',meters,age);
histogram(rhos1000(:,2),30)
Most of the values for
rhos1000
fall within the interval [0.92,0.98]. Since the
correlation coei cients for the resampled data sets (in our example) have
an approximately normal distribution, we can use their mean as a good
estimate for the true correlation coei cient.
mean(rhos1000(:,2))
ans =
0.9557
h is value is similar to our i rst result of
r
=0.9557, but now we have coni dence
in the validity of this result. In our example, however, the distribution of
the bootstrap estimates of the correlations from the age-depth data is quite
skewed, as the upper limited is i xed at one. Nevertheless, the bootstrap
method is a valuable tool for assessing the reliability of Pearson's correlation
coei cient for bivariate analysis.
4.3 Classical Linear Regression Analysis
Linear regression of ers another way of describing the relationship between
the two variables
x
and
y
. Whereas Pearson's correlation coei cient provides
only a rough measure of a linear trend, linear models obtained by regression
analysis allow the prediction of arbitrary
y
-values for any given value of
x
within the data range. Statistical testing of the signii cance of the linear
model provides some insights into the accuracy of these predictions.
Classical regression
assumes that
y
responds to
x
and that the entire
dispersion in the data set is contained within the
y
-value (Fig. 4.4). h is
means that
x
is then the independent variable (also known as the predictor
variable, or the regressor). h e values of
x
are dei ned by the experimenter
