An easiest way to solve "The general Trend Equation" for a time series
- 1. The General Trend Equation easy way Year Sales Visitors 2011 59,586,865.701 21056 2012 63,586,865.20 22544 2013 69,146,590.30 17493 2014 75,833,718.40 24945 2015 83,133,971.20 28427 2016 64,626,260.30 17927 2017 95,246,656.40 25490
- 2. Solution Thecompany will use the general trend equation in order to estimate the sales and visitors as below. Y = a + b x Rules Where b = ــــــــــــ ∑ Y n a = ــــــــــــ ∑ xy ∑ x ₂ ᶺ
- 3. Estimate Sales for Years 2018,2019,2020,2021 Year Sales X XY x 2011 59,586,865.701 -3 -178,760,597.10 9 2012 63,586,865.20 -2 -127,173,730.40 4 2013 69,146,590.30 -1 -69,146,590.30 1 2014 Base Year 75,833,718.40 0 0.00 0 2015 83,133,971.20 1 83,133,971.20 1 2016 64,626,260.30 2 129,252,520.60 4 2017 95,246,656.40 3 285,739,969.20 9 511,160,927.501 0 123,045,543.20 28 ₂
- 4. Y = a + b x Rules Where b = ــــــــــــ ∑ Y n a = ــــــــــــ ∑ xy ∑ x ₂ ᶺ a = ـــــــــــــــــــــــ 511,160,927.501 7 a = 73,022,989.64 b = ــــــــــــ 123,045,543.20 ـــــــــــ 28 b = 43,944,83.686 Y = 73,022,989.64 + 43,944,83.686 (X) where x estimated Year ᶺ
- 5. Estimate Sales for Years 2018,2019,2020,2021 Year 2018 “Base Year – Estimated Year” 2018-2014 = 4 , X= 4 Y = 73,022,989.64 + 43,944,83.686 (4) = 90,600,924.384ᶺ Year 2019 “Base Year – Estimated Year” 2019-2014 = 5 , X= 5 Y = 73,022,989.64 + 43,944,83.686 (5) = 94,995,408.07 Year 2020 “Base Year – Estimated Year” 2020-2014 = 6 , X= 6 Y = 73,022,989.64 + 43,944,83.686 (6) = 99,389,891.756 Year 2021 “Base Year – Estimated Year” 2021-2014 = 7 , X= 7 Y = 73,022,989.64 + 43,944,83.686 (7) = 103,784,375.442
- 6. Estimate number of visitors for Years 2018,2019,2020,2021 Year No of Visitor X XY x 2011 21056 -3 -63168 9 2012 22544 -2 -45088 4 2013 17493 -1 -17493 1 2014 Base Year 24995 0 0 0 2015 28427 1 28427 1 2016 17927 2 35854 4 2017 25490 3 76470 9 157932 0 15002 28
- 7. Y = a + b x Rules Where b = ــــــــــــ ∑ Y n a = ــــــــــــ ∑ xy ∑ x ₂ ᶺ a = ـــــــــــــــــــــــ157932 7 a = 22561.71 b = ــــــــــــ 15002 ـــــــــــ 28 b = 535.79 Y = 22561.71 + 535.79 (X) where x estimated Year ᶺ
- 8. Estimate Sales for Years 2018,2019,2020,2021 Year 2018 “Base Year – Estimated Year” 2018-2014 = 4 , X= 4 Y = 22562 + 536 (4) 24706ᶺ Year 2019 “Base Year – Estimated Year” 2019-2014 = 5 , X= 5 Y = 22562 + 536 (5 ) 25242 Year 2020 “Base Year – Estimated Year” 2020-2014 = 6 , X= 6 Y = 22562 + 536 (6) 25778 Year 2021 “Base Year – Estimated Year” 2021-2014 = 7 , X= 7 Y = 22562 + 536 (7) 26314