Question

In: Statistics and Probability

Jace collected the following data on the quarterly room occupancy (in hundreds) for a resort hotel...

  1. Jace collected the following data on the quarterly room occupancy (in hundreds) for a resort hotel in Iowa.

Year

quarter

Occupancy

2013

1

16

2

21

3

9

4

18

2014

1

15

2

20

3

10

4

18

2015

1

17

2

24

3

13

4

22

2016

1

17

2

25

3

11

4

21

2017

1

18

2

26

3

14

4

25

  1. Plot the data and describe any trend and seasonal effects you observe in the data.

  1. Compute and interpret the seasonal indices.
  1. Jace’s manager, Joseph, wants Jace to forecast the occupancy for four quarters of 2018. Can you help him (Forecast he room occupancy for four quarters of 2018)?

Solutions

Expert Solution

A.

In this graph, we see that there is an increasing trend in this data..and there is seasonality in the data.. The Occupancy rate drops every 3rd quarter and then gradually increases and peaks in 2nd quarter.

B.

Occupancy
Year 2013 2014 2015 2016 2017 Average Seasonal Index
Quarter Q1-13 16 15 17 17 18 16.6 0.922
Q2-13 21 20 24 25 26 23.2 1.289
Q3-13 9 10 13 11 14 11.4 0.633
Q4-13 18 18 22 21 25 20.8 1.156
Average 16 15.75 19 18.5 20.75 18

Seasonal Index is calculated by dividing each Quarter Average by the Grand average of the entire data( which is 18 in this case)

So, For Q1, Seasonal Index, SI = 16.6/18 = 0.922

For Q2, Seasonal Index, SI = 23.2/18 = 1.289

For Q3, Seasonal Index, SI = 11.4/18 = 0.633

For Q4, Seasonal Index, SI = 20.8/18 = 1.156

This shows us that Q3 has the lowest Occupancy. It becomes better gradually and maxes in Q2

C.

Average Occupancy in 2013 = 16

Average Occupancy in 2014 = 15.8

Average Occupancy in 2015 = 19

Average Occupancy in 2016 = 18.5

Average Occupancy in 2017 = 20.8

Since it is an increasing trend, we can take CAGR to forecast occupancy in 2018.

CAGR = (Occupancy in 2017 /  Occupancy in 2013)(1/4) - 1 = (20.8/16)(1/4) - 1 = 5.8%

Now, Average Occupancy in 2018 will be 5.8% more than 2017, which will be equal to 20.8*(1+5.8%) = 22.0066

Now Forecast for each quarter is given by,

For Q1, Occupancy = Average Occupancy * Seasonal Index = 22.0066*0.922 = 20.295

For Q2, Occupancy = 22.0066*1.289 = 28.364

For Q3, Occupancy = 22.0066*0.633= 13.9375

For Q4, Occupancy = 22.0066*1.156 = 25.429


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