Geoscience Reference
In-Depth Information
Instead of using the equation for the regression line we can also use the
function
polyval
to calculate the
y
-values.
plot(meters,age,'o'), hold on
plot(meters,polyval(p,meters),'r'), hold off
Both of the functions
polyfit
and
polyval
are incorporated in the GUI
function
polytool
.
Movie
4.1
polytool(meters,age)
h e coei cients
p(x)
and the equation obtained by linear regression can
now be used to predict
y
-values for any given
x
-value. However, we can only
do this within the depth interval for which the linear model was i tted, i.e.,
between 0 and 20 meters. As an example the age of the sediment at a depth
of 17 meters is given by
polyval(p,17)
ans =
112.9946
h is result suggests that the sediment at 17 meters depth has an age of ca.
113 kyrs. h e goodness-of-i t of the linear model can be determined by
calculating error bounds. h ese are obtained by using an additional output
parameter
s
from
polyfit
as an input parameter for
polyconf
to calculate the
95% (
alpha
=0.05) prediction intervals.
[p,s] = polyfit(meters,age,1);
[p_age,delta] = polyconf(p,meters,s,'alpha',0.05);
plot(meters,age,'o',meters,p_age,'g-',...
meters,p_age+delta,'r--',meters,p_age-delta,'r--')
axis([0 20 0 140]), grid on
xlabel('Depth in Sediment (meters)')
ylabel('Age of Sediment (kyrs)')
h e variable
delta
provides an estimate for the standard deviation of the
error in predicting a future observation at
x
by using
p(x)
. Since the
plot
statement does not i t on one line we use an
ellipsis
(three periods, i.e.,
...
)
followed by
return
or
enter
to indicate that the statement continues on the
next line. h e plot now shows the data points, and also the regression line
and the error bounds of the regression (Fig. 4.5). h is graph already provides
some valuable information on the quality of the result. However, in many
cases a better understanding of the validity of the model is required and
more sophisticated methods for testing the coni dence in the results are
therefore introduced in the following sections.
