Project

Chapter 4

MARKET AND DEMAND ANALYSIS

1. We have to estimate the parameters a and b in the linear relationship Yt = a + bT Using the least squares method.
According to the least squares method the parameters are:

∑ T Y – n T Y b = ∑ T 2 – n T 2

a = Y – bT The parameters are calculated below: Calculation in the Least Squares Method
T
Y TY T 2
1 2,000 2,000 1
2 2,200 4,400 4
3 2,100 6,300 9
4 2,300 9,200 16
5 2,500 12,500 25
6 3,200 19,200 36
7 3,600 25,200 49
8 4,000 32,000 64
9 3,900 35,100 81
10 4,000 40,000 100
11 4,200 46,200 121
12 4,300 51,600 144
13 4,900 63,700 169
14
5,300 74,200 196
∑ T = 105 ∑ Y = 48,500 ∑ TY = 421,600 ∑ T 2 = 1,015
T = 7.5
Y = 3,464

∑ T Y – n T Y 421,600 – 14 x 7.5 x 3,464 b = = ∑ T 2 – n T 2 1,015 – 14 x 7.5 x 7.5

57,880 = = 254 227.5 a = Y – bT = 3,464 – 254 (7.5) = 1,559 Thus linear regression is Y = 1,559 + 254 T
2. In general, in exponential smoothing the forecast for t + 1 is Ft + 1 = Ft + α et Where Ft + 1 = forecast for year ) α = smoothing parameter et = error in the forecast for year t = St = Ft F1 is given to be 2100 and α is given to be 0.3 The forecasts for periods 2 to 14 are calculated below:
Period t Data (St) Forecast (Ft) Error
(et St =Ft) Forecast for t + 1
(Ft + 1 = Ft + α et)

1 2,000 2100.0 -100 F2 = 2100 + 0.3 (-100) = 2070
2 2,200 2070 130 F3 = 2070 + 0.3(130) = 2109
3 2,100 2109.0 -9 F4 = 2109 + 0.3 (-9) = 2111.7
4 2,300 2111.7 188.3 F5 = 2111.7 + 0.3(188.3) = 2168.19
5 2,500 2168.19 331.81 F6 = 2168.19 + 0.3(331.81) = 2267.7
6 3,200 2267.7 932.3 F7 = 2267.7 + 0.3(9332.3) = 2547.4
7 3,600 2547.4 1052.6 F8 = 2547.4 + 0.3(1052.6) = 2863.2
8 4,000 2863.2 1136.8 F9 = 2863.2 + 0.3(1136.8) = 3204.24
9 3,900 3204.24 695.76 F10 = 33204.24 + 0.3(695.76) = 3413.0
10 4,000 3413 587.0 F11 = 3413.0 + 0.3(587) = 3589.1
11 4,200 3589.1