The least square method
- 1. THE LEAST SQUARE METHOD Introduction: First of all, you must find the figures of your company: the turnover (CA) of the last 5 years. Then add them in a data table. For example: Years 2007 2008 2009 2010 2011 1 Turnover K€ 80 162 250 300 408 Draw an adjusted line on a chart with: - The years in abscissa (xi) - The turnover in ordinate (yi) Adjusted line 450 400 350 300 250 200 150 100 50 0 2006 2006,5 2007 2007,5 2008 2008,5 2009 2009,5 2010 2010,5 2011 The purpose of this method is to find statistically the equation of the line y = ax + b since a data table.
- 2. I. The mathematical formulas a = ∑ xi yi – n x y ∑ xi² - n x ² a equals sum of xi times yi minus n times the x values times the y values divided by sum of xi exponent 2 minus n times the x values exponent 2 2 b=y–ax b equals the y values minus a times the x values n means the number of years taken in account II. The data table and calculations xi yi xi² xiyi 1 80 1 80 2 162 4 324 3 250 9 750 4 300 16 1200 5 408 25 2040 ∑ 15 ∑ 1200 ∑ 55 ∑ 4394 In column 1 of the table: xi You transform the years in numbers. For example: 2007 = 1 2008 = 2 2009 = 3 etc…
- 3. In column 2 of the table: yi You enter the turnover in K€ In column 3 of the table: x² You multiply: xi xi In column 4 of the table, you multiply : xi yi At the ends of each column, calculate its sum. Then, 3 You calculate: x = ∑ xi / n = 15/5= 3 the x values equal the average of xi y = ∑ yi / n = 1200/5= 240 the y values equal the average of yi III. Solving of the equation y = ax + b with the mathematical formulas a = 4394 – ( 5 x 3 x 240) 55 – (5 x 3²) a = 794 = 79,4 10 b = 240 – (79,4 x 3) b = 1,8
- 4. The equation of the adjusted line is: y = ax +b y = (79,4 x 6) + 1,8 IF 2007 = 1 4 2008 = 2 2009 = 3 2010 = 4 2011 = 5 THEN 2012 = 6 y = 478,20 y = the estimated turnover for 2012 is 478 200 €