1 Chapter 13 Curve Fitting and Correlation This chapter will be concerned primarily with two separate but closely interrelated processes: (1) the fitting of experimental data to mathematical forms that describe their behavior and (2) the correlation between different experimental data to assess how closely different variables are interdependent.
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1
Chapter 13 Curve Fitting and Correlation
This chapter will be concerned primarily
with two separate but closely interrelated
processes: (1) the fitting of experimental data to mathematical forms that describe
their behavior and (2) the correlation
between different experimental data to
assess how closely different variables are
interdependent.
2
The fitting of experimental data to a
mathematical equation is called regression.
Regression may be characterized by different adjectives according to the
mathematical form being used for the fit
and the number of variables. For example,
linear regression involves using a straight-
line or linear equation for the fit. As another example, Multiple regression involves a
function of more than one independent variable.
3
Linear Regression
Assume n points, with each point having
values of both an independent variable x
and a dependent variable y.
1 2 3The values of are , , ,...., .nx x x x x
1 2 3The values of are , , ,...., .ny y y y y
A best-fitting straight line equation
will have the form
1 0y a x a
4
Preliminary Computations
0
1sample mean of the values
n
k
k
x x xn
0
1sample mean of the values
n
k
k
y y yn
2 2
1
1sample mean-square of the values
n
k
k
x x xn
1
1sample mean of the product
n
k k
k
xy xy x yn
5
Best-Fitting Straight Line
1 22
xy x ya
x x
2
0 22
x y x xya
x x
0 1Alternately, a y a x
1 0y a x a
6
Example 13-1. Find best fitting straight line equation for the data shown below.