Least square method of population projection soniya Junior Member  Posts: 34 Threads: 18 Joined: Aug 2014 Reputation: 0 11-14-2014, 08:43 AM Least square method of population projection This method is applicable when time-series data is available. It is a simple method commonly used to make future projections on the basis of the past trend. It is common to fit a straight line to the past observations. y= a+bx a= ƩY / N b= Ʃxy /x2 y= last five year decades population x= -2,-1,0,1,2 N= 5 (for five year population data) Manish Jain Super Moderator      Posts: 194 Threads: 142 Joined: Mar 2014 Reputation: 1 11-18-2018, 06:50 AM (This post was last modified: 11-18-2018, 09:36 AM by Manish Jain.) Example of Least square method of population projection Given Data Year            population (in million) 1997           51.99 1998           52.49 1999           55.12 2000           54.07 2001           57.56 ΣY = Na + b. Σ X ΣXY = a. Σ X + b. ΣX2 where: ΣX = the sum of all observations of X ΣY = the corresponding sum of all the Y observations ΣXY = the sum of all the products of X and Y ΣX2 = the sum of all the squares of X N = total number of observations Population  Projections Based on Method of Least Squares  Year          population   S. No. of           Square of                 (in million)       Col. 1                   ‘X’                       (Y)                   (X)                                                      X.Y 1997                51.99             1                       1                              51.99 1998                52.46             2                       4                              104.92 1999                55.12             9                      1                               65.36 2000               54.07              4                      16                             216.23 2001                57.56             5                       25                            287.80 Total     (ΣY) 271.20           (ΣX) 15           (ΣX2) 55                  ΣXY) 826.35 By using the following two equations, the value of Y = a + b . X can be calculated: ΣY = Na + bΣ X =  271.20 = 5a + 15b ……………………………1 ΣXY = a Σ X + b ΣX2 =  826.33 = 15a + 55b ……………………………….2 Multiply equation (1) by 3 and subtract it from Equation (2) to get the value of ‘b’. By putting the value of ‘b’ in Equation (2), the value of ‘a’ can also be worked out:  Thus, by interpolation we get the following equation:  Y = 50.43 + 1.27 X (with 1997 as X=1)  In the above example, by putting the values of ‘X’ we can get values for various years to draw the best-fitting lines and then project it in the future. Accordingly, the population projections for 2002 can be worked out as under:  population in 2002 (Y) = 50.43 + 1.27 x 6 = 58.05, X = 6 in year 2002-03 Manish Jain Luhadia  B.Arch (hons.), M.Plan Email: manish@frontdesk.co.in Tel: +91 141 2743536 « Next Oldest | Next Newest »