Least square method (sometimes called regression model) is a statistical approach to estimate an expected value or function with the highest probability from the observations with random errors. The highest probability is replaced by minimizing the sum of square of residuals in the least square method.
Residual is defined as the difference between the observation and an estimated value of a function.
In GIS, the least square method is widely used for spatial data analysis rather than single use of interpolation technique.
Least square method is commonly applied for the following two cases in GIS.
Curve Fitting
In case measurements (xi, yi ) are given, the relationship between x and y is estimated by a function, for example: y = f (x) = ax + b. By minimizing the square sum of residuals, the unknown parameters a and b will be determined.
Unknown parameters in the case of y = ax+ b are determined as follows.
Observed Equation; AX = B or xi a + b = yi