Graphics Programs Reference
In-Depth Information
subplot(1,2,1), bar(v,n_syn,'r')
subplot(1,2,2), bar(v,n_exp,'b')
Visual inspection of the bar plots reveals similarities between the data sets.
Hence, the
-test can be used to test the hypothesis that the residuals follow
a gaussian distribution.
χ
2
chi2 = sum((n_exp - n_syn).^2 ./n_syn)
chi2 =
2.3465
The critical
2
test requires the
degrees of freedom
df
, which is the number of classes reduced by one and
the number of parameters estimated. In our example, we test for a gaussian
distribution with two parameters, mean and standard deviation. Therefore the
degrees of freedom is
df
=6-(1+2)=3. We test at a 95% signifi cance level:
χ
2
can be calculated by using
chi2inv
. The
χ
chi2inv(0.95,3)
ans =
7.8147
The critical
of 2.3465. It is not
possible to reject the null hypothesis. Hence, we conclude that our residuals
follow a gaussian distribution and the bivariate data set is well described by
the linear model.
χ
2
of 7.8147 is well above the measured
χ
2
4.6 Bootstrap Estimates of the Regression Coeffi cients
We use the
bootstrap
method to obtain a better estimate of the regression
coeffi cients. Again, we use the function
bootstrp
with 1000 samples
(Fig. 4.6).
p_bootstrp = bootstrp(1000,'polyfit',meters,age,1);
The statistics of the fi rst coeffi cient, i.e., the slope of the regression line is
hist(p_bootstrp(:,1),15)
mean(p_bootstrp(:,1))
ans =
5.6023
std(p_bootstrp(:,1))
