Stat2225 | Assignment 5 | Question 1 Solution

Use SGC wherever appropriate, make sure include the SGC output and graphs.

1. [18 marks]

The following data report the occupancy rates (%) and average room rates ($) for the largest U.S. hotel markets (The Wall Street Journal Almanac 1998). We would like to know the linear relationship between the two rates with the occupancy rate in terms of average room rate.

Room                                           Occupancy                                              Average

Market                                                          Rate (%)                                     Rate ($)

Los Angeles-Long Beach                     67.9                             75.91

Chicago                                               72.0                             92.04

Washington                                          68.4                             94.42

Atlanta                                                 67.7                             81.69

Dallas                                                  69.5                             74.76

San Diego                                            68.7                             80.86

Anaheim-Santa Ana                             69.5                             70.04

San Francisco                                      78.7                             106.47

Houston                                               62.0                             66.11

Miami-Hialeah                                     71.2                             85.83

Oahu Island                                         80.7                             107.11

Phoenix                                               71.4                             95.34

Boston                                                 73.5                             105.51

Tampa-St. Petersburg                           63.4                             67.45

Detroit                                                 68.7                             64.79

Philadelphia                                         70.1                             83.56

Nashville                                             67.1                             70.12

Seattle                                                  73.4                             82.60

Minneapolis-St. Paul                            69.8                             73.64

New Orleans                                        70.6                             99.00

1. Write out the estimated linear regression equation in the context of the problem.[2]
2. Are the two rates correlated? Justify it by testing the slope. Interpret your result. (Don’t forget to write the hypotheses, and don’t use the correlation coefficient as you have done in 1181)[3]
3. Provide a 95% interval estimate of the real average occupancy rate with an average room rate of $90. Interpret the interval.[5]
4. Provide a 95% interval estimate of the real occupancy rate with an average room rate of $90. Interpret the interval.[4]
5. Are the data homoscedastic? Justify it by using the appropriate graph and interpret the result.[3]
6. How does the result in part (e) affect parts (c) and (d)?[1]