Page 255 - Computational Statistics Handbook with MATLAB

Chapter 7: Data Partitioning 243

the importance of looking at scatterplots, because it is obvious from the plots
that the relationships between the variables are not similar. The scatterplots
are shown in Figure 7.3.
% Here is another example.
% We have 4 data sets with essentially the same
% correlation coefficient.
% The scatterplots look very different.
% When this file is loaded, you get four sets
% of x and y variables.
load anscombe
% Do the scatterplots.
subplot(2,2,1),plot(x1,y1,'k*');
subplot(2,2,2),plot(x2,y2,'k*');
subplot(2,2,3),plot(x3,y3,'k*');
subplot(2,2,4),plot(x4,y4,'k*');
We now determine the jackknife estimate of bias and standard error for ρ ˆ
using csjack.

% Note that 'corr' is something we wrote.
[b1,se1,jv1] = csjack([x1,y1],'corr');
[b2,se2,jv2] = csjack([x2,y2],'corr');
[b3,se3,jv3] = csjack([x3,y3],'corr');
[b4,se4,jv4] = csjack([x4,y4],'corr');
The jackknife estimates of bias are:
b1 = -0.0052
b2 = 0.0008
b3 = 0.1514
b4 = NaN
The jackknife estimates of the standard error are:
se1 = 0.1054
se2 = 0.1026
se3 = 0.1730
se4 = NaN
Note that the jackknife procedure does not work for the fourth data set,
because when we leave out the last data point, the correlation coefficient is
undefined for the remaining points.

The jackknife method is also described in the literature using pseudo-val-
ues. The jackknife pseudo-values are given by

) i – ()
,
,
–
T i = nT ( n – 1)T i = 1 … n , (7.12)
© 2002 by Chapman & Hall/CRC