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.
where a0, and a1 indicate any real numbers.
To establish the fitted equation, the values of a0, a1 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.
Find the partial derivatives for a0 and a1 respectively through functionso as to make the derivatives equal to zero:
Obtain the solutions for a0 and a1 as well as the correlation coefficient. It is observed that the closer the correlation coefficient R is to 1, the better the model fits.
In (Equation 10), m is the sample size, that is, the number of experiments; xi and yi are the values of any set of experiments x and y, respectively.