Question 10.85

10.85 Hotel sizes and numbers of employees.

A human resources study of hotels collected data on the size, measured by number of rooms, and the number of employees for 14 hotels in Canada.22 Here are the data.

hotsize

Employees Rooms Employees Rooms
1200 1388 275 424
180 348 105 240
350 294 435 601
250 413 585 1590
415 346 560 380
139 353 166 297
121 191 228 108

529

  1. To what extent can the number of employees be predicted by the size of the hotel? Plot the data and summarize the relationship.
  2. Is this the type of relationship that you would expect to see before examining the data? Explain why or why not.
  3. Calculate the least-squares regression line and add it to the plot.
  4. Give the results of the significance test for the regression slope with your conclusion.
  5. Find a 95% confidence interval for the slope.

10.85

(a) The relationship is linear, positive, and strong. (b) Yes, a bigger hotel requires more employees to take care of both the rooms and the guests, so we would expect a positive slope. (c) . (d) . There is a significant linear relationship between the number of employees and the number of rooms for hotels. (e) (0.25259, 0.77459).