Question

8) The Bayside Fountain Hotel is adjacent to County Coliseum, a 24,000-seat arena that is homel the city's professional basketball and ice hockey teams and that hosts a variety of concerts shows, and conventions throughout the year. The hotel has experienced the following ocupunr rates for the past 9 years, since the coliseum opened:

Answer 1

Exponential smoothing

13 Year(x)Occupancy rate (y) Forecast Eror Abs(error) 83 78 75 81 86 8581.7443.256 8982.39526.6048 6.6048 90 83.71616 6.283846.28384 86 84.97293 1.027072 1.027072 83 83 82 80.6 80.68 15 16 7 5.32 3.256 18 19 5.32 23 Average 24 25 1.361464 4.361464

Forecast F(t) = Alpha * A(t-1) + (1-Alpha)*F(t-1)

Average Error = 1.361464

MAD = Abs(Error)/n = 4.361464

Adjusted exponential smoothing

1 Yearx) lOccupancy rate (y) Ft Tt FITt Error Abs(error) 83 78 75 81 86 80,1744 0.43072 79.74368 6.25632 6.25632 85 80.99494 0.18047 80.81448 4.185523 4.185523 8981.651580.01305 81.638547.361465 7.361465 90 83.11083 0.281412 83.392246.60776 6.60776 86 84.713790.545723 85.259520.740485 0.740485 83 83 82 80.44 83 83 81.8 0.472 79.968 1.032 1.032 10 11 Average 12 1.797944 4.747944

F(t) = FIT(t-1)+alpha*(A(t-1) – FIT(t-1)

T(t) = T(t-1) + beta*(F(t) – FIT(t-1))

FIT(t) = F(t) + T(t)

Average Error = 1.797944

MAD = Abs(Error)/n = 4.747944

Linear trend line forecast

	Year(x)	Occupancy rate (y)	xy	x2
	1	83	83	1
	2	78	156	4
	3	75	225	9
	4	81	324	16
	5	86	430	25
	6	85	510	36
	7	89	623	49
	8	90	720	64
	9	86	774	81
Total	45	753	3845	285

x-bar = Sum(x)/n = 45/9 = 5

y-bar = Sum(y)/n = 753/9 = 83.66667

b = (Sum(xy) – n*x-bar*y-bar)/(Sum(x²) – n*x-bar*x-bar) = (3845-9*5*83.66667)/(285 – 9*5*5)

                = 79.99985/60= 1.333331

a = y-bar –b*x-bar

= 83.66667 - 1.333331*5 = 77.000015

Regression equation is y = a + bx,

we get following regression equation by substituting values of a and b

Regression equation is y =77.000015 + 1.333331x

Yearx) Occupancy rate Abs(error) 4.6666540 4.6666540 1.6666770 1.6666770 6.0000080 6.0000080 1.3333390 1.3333390 2.3333300 2.3333300 0.0000000 0.0000000 2.6666680 2.6666680 2.3333370 2.3333370 2.9999940 2.9999940 0.0000290 24.0000070 3.222E-06 2.6666674 Forecast Error 1 78.33335 479.66668 9 81.00001 16 82.33334 25 83.66667 85 49 86.33333 64 87.66666 81 88.99999 83 78 75 81 86 85 89 90 86 753 83.66666667 83 156 225 324 430 510 623 720 774 3845 36 10 11 Tota 12 Average 45 285

Average Error = -3.222E-06

MAD = Abs(error)/n = 2.6666674

Comparing all three forecasts, Linear trend line forecast is better as it has lowest Average Error and lowest MAD