# Methods of Projection

Topics: Projection, Line, Analytic geometry Pages: 5 (511 words) Published: January 31, 2013
Methods of Projection
I. Arithmetic Straight Line
Yc = a + Yi – 1
Where:
Yc = initial Value (1st year)
Yn = Final Value (last year)
N = number of years
Yi = value for the year past

a = Yn - Yc
N – 1
= 5975147 – 5413182
5 – 1
= 140, 491.25

Historical Values

|  |Y |a |Yi – 1 |Yc |Y – Yc |(Y –Yc)2 | |2009 |5413182 |--- |--- |--- |0 |0 | |2010 |5548508 |140491.25 |5413182 |5553673.25 |-5165.25 |26679807.56 | |2011 |5687171 |140491.25 |5553673.25 |5694164.5 |-6993.5 |48909042.25 | |2012 |5829384 |140491.25 |5694164.5 |5834655.75 |-5271.75 |27791348.06 | |2013 |5975147 |140491.25 |5834655.75 |5975147 |0 |0 |

( = 103380197.9
( = 4,547.0913

Projected Values

|  |a |Yi – 1 |Yc | |2014 |140491.25 |5975147 |6115638.25 | |2015 |140491.25 |6115638.25 |6256129.5 | |2016 |140491.25 |6256129.5 |6396620.75 | |2017 |140491.25 |6396620.75 |6537112 | |2018 |140491.25 |6537112 |6677603.25 |

II. Arithmetic Geometric Curve
Yc = Yi – 1
1 + r
Where Yi + 1 = value for the year ahead
r = average rate of increase

r = ( % Increase
N – 1
= 10= 2
5
Historical values
|  |Y |% Increase (Decrease) | |2014 |5975147 |1.2 |7170176.4 | |2015 |7170176.4 |1.2 |8604211.68 | |2016 |8604211.68 |1.2 |10325054.02 | |1017 |10325054.02 |1.2 |12390064.82 | |2018 |12390064.82 |1.2 |14868077.78 |

III. Statistical Straight Line
Yc = a + bx

Where a = (Y - b (x= 28453392 -140480.6*15=5269236.6
n n5 5

b = n ( XY - (X (Y = 5*86764982 – 15*28453392= 140480.6 n (X2 – (( X) 25*55(55)2

|  |Y |X |X2 |XY | |2014 |5269236.6 |140480.60 |6 |6112120.20 | |2015 |5269236.6 |140480.60 |7 |6252600.80 | |2016 |5269236.6 |140480.60 |8 |6393081.40 | |1017 |5269236.6 |140480.60 |9...