Linear Regression:
The process for obtaining the best fit is frequently called the "regression". Linear regression stands for straight line fitting of data.
Linear approximations are frequently satisfactory in a broad variety of engineering applications.
If we choose a straight line for curve fitting as:
f (x) = a + bx, here a & b are coefficients to be find out. Then for "best fit", the sum S that is to be minimized will be
The minimum tale place when
These might be simplified & expressed like following
These two simultaneous equations might be solved to get the coefficients a and b. The resulting equation f (x) = a + bx then gives the best fit straight line to the specified data. The spread of data before regression applied might be n,
Here yavg might be average or mean of the specified data. The extent of development because of curve fitting is specified by the expression
Here r is the correlation coefficient.
It might be noted down that r contain a maximum value of 1.0. Its value shall be greater for good correlation!