People involved in the tourism industry are interested in many aspects of tourist behaviour. An aspect that may be of interest is whether there is a relationship between demand for tourists, as measured by the number of guest nights, and the number of tourist accommodation establishments.

Using the following data provided by Statistics New Zealand, develop a model to predict the number of guest establishments using the number of guest nights. Interpret the slope and intercept of the model. Do they make sense? What do the p-value and r² suggest about the strength of the relationship? Suppose that there is a serious health scare in New Zealand and, as a result, guest nights fall dramatically to 500 while the number of guest establishments decreases slightly to 3850. If this extra observation is included in the estimation sample, how are the SSE, standard error and slope term affected? Is the new model appropriate for predicting the number of guest establishments? Why or why not?

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Guest nights ('000) Month Number of guest establishments Jan. 3863 4364 Feb. 3876 3493 Mar. 3877 3399 Apr. May 3860 2814 3780 1942 3713 June 1809 July Aug. Sept. 3686 2205 3723 2131 3790 2286 Oct. 3878 2439 Nov. 3937 2795 Dec. 3970 3239