Graphics Programs Reference
In-Depth Information
1st Regression Coefficient
2st Regression Coefficient
200
200
Slope = 5.6±0.4
Y Intercept = 1.3±4.4
150
150
100
100
50
50
0
0
4
5
6
7
−10
0
10
20
Slope
Y−Axis Intercept
a
b
Fig. 4.6
Histogram of the
a
fi rst (
y
-axis intercept of the regression line) and
b
second (slope
of the line) regression coeffi cient as estimated from bootstrap resampling. Whereas the fi rst
coeffi cient is very-well constrained, the second coeffi cient shows a large scatter.
ans =
0.4421
Your results might be slightly different due to the different state of the built-
in random number generator used by
bootstrp
. The relatively small stan-
dard deviation indicates that we have an accurate estimate. In contrast, the
statistics of the second parameter shows a signifi cant dispersion.
hist(p_bootstrp(:,2),15)
mean(p_bootstrp(:,2))
ans =
1.3366
std(p_bootstrp(:,2))
ans =
4.4079
The true values as used to simulated our data set are 5.6 for the slope and
1.2 for the intercept with the
y
-axis, whereas the coeffi cients calculated us-
ing the function
polyfit
were 5.6393 and 0.9986, respectively. We see
that indeed the intercept with the
y
-axis has a large uncertainty, whereas the
slope is very well defi ned.
