least when compared with other fitting methods. So, this method is known as the Method of Least Squares and satisfies the following conditions: (i) The sum of the deviations of the actual values of Y and Ŷ (estimated value of Y ) is Zero. that is Σ( Y–Ŷ ) = . (ii) The sum of squares of the deviations of the actual values of Y and Ŷ (estimated value of Y ) is least.
that is Σ( Y – Ŷ ) is least. XII Std - Business Maths & Stat EM Chapter - - Procedure: (i) The straight line trend is represented by the equation Y = a + bX … ( ) where Y is the actual value, X is time, a, b are constants (ii) The constants ‘ a ’ and ‘ b ’ are estimated by solving the following two normal Equations ΣY = n a + b ΣX ... ( ) Σ XY = a ΣX + b ΣX ... ( ) Where ‘ n ’ = number of years given in the data.
(iii) By taking the mid-point of the time as the origin, we get ΣX = (iv) When ΣX = , the two normal equations reduces to ΣY = n a + b ( ); a Y Y ΣXY = a ( ) + b ΣX ; b XY