Merits of Least Square Method
(i) This method is completely free from personal bias of the analyst as it is very objective in nature. Any body using this method is bound to fit the same type of straight line, and find the same trend values for the series.
(ii) Unlike the moving average method, under this method, we are able to find the trend values for the entire time series without any exception for the extreme periods of the series even.
(iii) Unlike the moving average method, under this method, it is quite possible to forecast any past of future values perfectly, since the method provides us with a functional relationship between two variables in the form of a trend line equation, viz. Yc = a + bX, Yc = a + bX + cX² + …. Or Yc = abX etc.
(iv) This method provides us with a rate of growth per period i.e. b, as shown in the equations cited above. With this rate of growth, we can very well determine the value for any past or previous year by the process of successive addition, or deduction from the trend values of the origin of X.
(v) This method providers us with the line of the best fit from which the sum of the positive and negative deviation is zero, and the sum of the squares of the deviations is least i.e.
(i) ∑ (Y-Yc) = 0 ; and (ii) ) ∑ (Y-Yc)2 = The least values.
(vi) This method is the most popular, and widely used for fitting mathematical function to a given set of observations.
This method is very flexible in the sense that it allows for shifting the trend origin from one point of time to another, and for the conversion of the annual trend equation into monthly, or quarterly trend trend equation, and vice versa.
