Question

of de cios Toronto Towers Plaza Hotel SOLVED PROBLEM 4.5 Room registrations in the Toronto Towers PL have been recorded for the past 9 years. To project future occupancy, management would like to determine the math. ematical trend of guest registration. This estimate will help the hotel determine whether future expansion will be needed. Given the following time-series data, develop a regression equation relating registrations to time (e.g., a trend equation). Then forecast year 11 registrations. Room registrations are in the thousands: Year 1: 17 Year 6: 20 Year 2:16 Year 3: 16 Year 4:21 Year 5:20 Year 7:23 Year 8: 25 Year 9: 24

Answer 1

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To calculate the regression equation we need to calculate the values of x² and xy which can be calculated as follows:3

Year	Transformed year, x	Registrants, y (In thousands)	x2	xy
1	1	17	1	17
2	2	16	4	32
3	3	16	9	48
4	4	21	16	84
5	5	20	25	100
6	6	20	36	120
7	7	23	49	161
8	8	25	64	200
9	9	24	81	216
	$\small \sum$x = 45	$\small \sum$y = 182	$\small \sum$x2= 285	$\small \sum$xy = 978

$\small \overline{x}$= $\small \sum$ x / n = 45 / 9 = 5

$\small \overline{y}$ = $\small \sum$ y /n = 182 / 9 = 20.22

b = $\small \sum$ xy

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