least square method While investigating the correlation between variables, we get a series of paired data through actual measurements. Plot these data on the x – y coordinates, then a scatter diagram as shown in Figure 1 will be obtained. It can be observed that the points are in the vicinity of a curve, whose fitted equation is set as the following Equation 1.
Figure
1
Equation 1 where a_{1}_{ }indicate any
real numbers.To establish the fitted equation, the values of a_{1}_{ }and k
need to be determined via subtracting the calculated valuefrom the measured value, i.e., via.Then calculate the quadratic sum of mas shown in Equation 2.
把(式1)代入(式2)中，如式 3：
Find the partial derivatives for a_{1}_{ } respectively through functionso as to make the derivatives equal to zero:
Derivation：
Derivation：
Obtain the solutions
for a In (Equation 10), m is the
sample size, that is, the number of experiments; x |