Physics and Engineering of Radiation Detection

9.7. Regression 555

The standard deviation of the mean is given by

σ 12 =

[

σ^21

N 1

+

σ^22

N 2

] 1 / 2

=

[

17. 612

5

+

20. 592

6

] 1 / 2

=11. 52.

Now we are ready to compute thetvalue.

t =

| 396. 2 − 394 |

11. 52

=0. 191

To compare thistvalue with the tabulated values we must first determine the

degrees of freedom of the dataset. This is given by

ν = N 1 +N 2 − 2

=5+6−2=9.

For a 95% confidence level and 9 degrees of freedom the tabulatedtvalue is

2.26. And for a 99% confidence level the tablulatedtvalue is 1.83. Since

both of these values are greater than the calculatedtvalue of 0.19, therefore

we can say with at least 99% confidence that the two dataset means are not

significantly different.

9.7 Regression.................................

Regression analysis is perhaps the most widely used technique to draw inferences
from experimental data. The basic idea behind it is to fit a function that closely
represents the trend in the data. The function can then be used to make predictions
about the variables involved.
Fitting a function to the data through regression analysis is not always a very
pleasant experience, specially if the data shows variations that can not be charac-
terized by standard functions, such as polynomial, exponential, or logarithmic. The
easiest form of regression analysis is the simple linear regression, which we will dis-
cuss in some detail now. Later on we will look at other kinds of regression analysis.

9.7.A SimpleLinearRegression

Simple linear regression refers to fitting a straight line to the data. The fitting
is mostly done using a technique calledleast square fitting. To understand this
technique, let us start with the equation of a straight line

y=mx+c, (9.7.1)

wheremis the slope of the line andcis itsy-intercept. Since slope andy-intercept
determine the orientation and position of the straight line on thexy-plot, therefore