Least Squares Method

# Least Squares Method - 140(7(42 a = y bx = 98.86 10.54(4 =...

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1 Least Squares Method Time period Values of Dependent Variable Figure 4.4 Deviation 1 Deviation 5 Deviation 7 Deviation2 Deviation 6 Deviation 4 Deviation 3 Actual observation (y value) Trend line, y = a + bx ^

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2 Least Squares Method Time period Values of Dependent Variable Figure 4.4 Deviation 1 Deviation 5 Deviation 7 Deviation2 Deviation 6 Deviation 4 Deviation 3 Actual observation (y value) Trend line, y = a + bx ^ Least squares method minimizes the sum of the squared errors (deviations)
3 Least Squares Method Equations to calculate the regression variables b = Σ xy - nxy Σ x 2 - nx 2 y = a + bx ^ a = y - bx

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4 Least Squares Example b = = = 10.54 xy - nxy x 2 - nx 2 3,063 - (7)(4)(98.86) 140 - (7)(42) a = y - bx = 98.86 - 10.54(4) = 56.70 Time Electrical Power Year Period (x) Demand x 2 xy 1999 1 74 1 74 2000 2 79 4 158 2001 3 80 9 240 2002 4 90 16 360 2003 5 105 25 525 2004 6 142 36 852 2005 7 122 49 854 x = 28 y = 692 x 2 = 140 xy = 3,063 x = 4 y = 98.86
5 Least Squares Example b = = = 10.54 Σ xy - nxy Σ x 2 - nx 2 3,063 - (7)(4)(98.86)

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Unformatted text preview: 140 - (7)(42) a = y- bx = 98.86 - 10.54(4) = 56.70 Time Electrical Power Year Period (x) Demand x 2 xy 1999 1 74 1 74 2000 2 79 4 158 2001 3 80 9 240 2002 4 90 16 360 2003 5 105 25 525 2004 6 142 36 852 2005 7 122 49 854 x = 28 y = 692 x 2 = 140 xy = 3,063 x = 4 y = 98.86 The trend line is y = 56.70 + 10.54x ^ 6 Least Squares Example | | | | | | | | | 1999 2000 2001 2002 2003 2004 2005 2006 2007 160 150 140 130 120 110 100 90 80 70 60 50 Year Power demand Trend line, y = 56.70 + 10.54x ^ 7 Least Squares Requirements 1. We always plot the data to insure a linear relationship 2. We do not predict time periods far beyond the database 3. Deviations around the least squares line are assumed to be random...
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Least Squares Method - 140(7(42 a = y bx = 98.86 10.54(4 =...

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