Statistics Case Study
Executive Overview, Part I
The management staff at a hotel located in a popular Caribbean resort area is engaged in planning activities for the next year. Fundamental to any plans made will be the expected occupancy rate of the hotel. The management staff has extracted quarterly occupancy rates for the past 5 years from the hotel records to forecast the occupancy rates for quarters 1, 2, 3 and 4 of next year.
Observing that this is a time series problem, we first generated a time series plot of the occupancy rate. And we can see a seasonal pattern from the plot. (See Figure 1 in Appendix A) Given the data, since year and quarter are both qualitative variables, we first transferred each quarter in each year in to a period number. Quarter 1 in year 1 is period 1, quarter 2 in year 1 is period 2, and so on. So for quarters in year 6, the period will be 21, 22, 23 and 24. Then we used dummy variable for quarters. (See Table 1 in Appendix A) With these modified data, we ran a regression analysis and got the equation: Occupancy Rate = 0.558 + 0.00504 Period + 0.136 Quarter2 + 0.202 Quarter3 - 0.0035 Quarter4
Forecast for quarters in year 6
Quarter 1: 0.66384 (Rate= 0.558+0.00504*21)
Quarter 2: 0.80488 (Rate = 0.558+0.00504*22+0.136*1)
Quarter 3: 0.87592 (Rate = 0.558+0.00504*23+0.202*1)
Quarter 4: 0.67546 (Rate = 0.558+0.00504*24-0.0035*1)
Appendix A
Figure 1
A time-series data plot is most appropriate for Problem 1 because the data is collected over equal periods at regular intervals for more than one period of time. The data meets the requirement having a Seasonal Component (St) because the pattern of four quarterly periods regularly repeats itself for five years, yet the period is completed within one year, representing a seasonal pattern. The data also has an Irregular Component ( It) because it is not perfectly cyclical and has some unsystematic fluctuations.
Table 1
Table 2
Results for: Occupancy Rates Regression Analysis: Occupancy Rate
The management staff at a hotel located in a popular Caribbean resort area is engaged in planning activities for the next year. Fundamental to any plans made will be the expected occupancy rate of the hotel. The management staff has extracted quarterly occupancy rates for the past 5 years from the hotel records to forecast the occupancy rates for quarters 1, 2, 3 and 4 of next year.
Observing that this is a time series problem, we first generated a time series plot of the occupancy rate. And we can see a seasonal pattern from the plot. (See Figure 1 in Appendix A) Given the data, since year and quarter are both qualitative variables, we first transferred each quarter in each year in to a period number. Quarter 1 in year 1 is period 1, quarter 2 in year 1 is period 2, and so on. So for quarters in year 6, the period will be 21, 22, 23 and 24. Then we used dummy variable for quarters. (See Table 1 in Appendix A) With these modified data, we ran a regression analysis and got the equation: Occupancy Rate = 0.558 + 0.00504 Period + 0.136 Quarter2 + 0.202 Quarter3 - 0.0035 Quarter4
Forecast for quarters in year 6
Quarter 1: 0.66384 (Rate= 0.558+0.00504*21)
Quarter 2: 0.80488 (Rate = 0.558+0.00504*22+0.136*1)
Quarter 3: 0.87592 (Rate = 0.558+0.00504*23+0.202*1)
Quarter 4: 0.67546 (Rate = 0.558+0.00504*24-0.0035*1)
Appendix A
Figure 1
A time-series data plot is most appropriate for Problem 1 because the data is collected over equal periods at regular intervals for more than one period of time. The data meets the requirement having a Seasonal Component (St) because the pattern of four quarterly periods regularly repeats itself for five years, yet the period is completed within one year, representing a seasonal pattern. The data also has an Irregular Component ( It) because it is not perfectly cyclical and has some unsystematic fluctuations.
Table 1
Table 2
Results for: Occupancy Rates Regression Analysis: Occupancy Rate