Page 81 - MATLAB Recipes for Earth Sciences

4.5 Analyzing the Residuals 73

Plotting the residuals does not show obvious patterned behavior. Thus no

more complex model than a straight line should be fitted to the data.
plot(meters,res,'o')

An alternative way to plot the residuals is a stem plot using stem.
subplot(2,1,1)
plot(meters,age,'o'), hold
plot(meters,p(1) * meters + p(2),'r')
subplot(2,1,2)
stem(meters,res);

Let us explore the distribution of the residuals. We choose six classes and
calculate the corresponding frequencies.

[n_exp,x] = hist(res,6)
n_exp =
5 4 8 7 4 2

x =
-16.0907 -8.7634 -1.4360 5.8913 13.2186 20.5460
By basing the bin centers in the locations defined by the function hist, a

more practical set of classes can be defi ned.

v = -13 : 7 : 23
n_exp = hist(res,v);
Subsequently, the mean and standard deviation of the residuals are com-
puted. These are then used for generating a theoretical frequency distribu-
tion that can be compared with the distribution of the residuals. The mean
is close to zero, whereas the standard deviation is 11.5612. The function
normpdf is used for creating the frequency distribution n_syn similar to
our example. The theoretical distribution is scaled according to our original
sample data and displayed.
n_syn = normpdf(v,0,11.5612);

n_syn = n_syn ./ sum(n_syn);
n_syn = sum(n_exp) * n_syn;

The first line normalizes n_syn to a total of one. The second command
scales n_syn to the sum of n_exp. We plot both distributions for compari-
son.