$($a$)$ A hotel chain decides to use data on existing hotels to determine desirable locations for new hotels. Data on $90$ hotels in the chain have been collected in an attempt to understand operating margin. The variables are:

$-$ Operating margin $-$ the dependent variable, in $\%$

$-$ Indoor pool $-$ whether the hotel has a heated indoor pool, Yes $=1$ and No $=0$

$-$ Competitor rooms $-$ total number of competitor rooms in hotels within $3$ miles

$-$ Distance to competitor $-$ miles to nearest competitor hotel

$-$ Office space $-$ amount of office space available within $3$ miles, in

thousands of square feet

$-$ Distance to downtown $-$ miles to downtown $($the central part of a city or town$).$

Selected SPSS output is provided in Figure $1($on the next page$).$ Analyse the regression results, making sure you first write out the full regression model, including any assumptions, and the estimated model. In light of the regression results, propose any changes you would make to the model, including any other explanatory variables which you would consider using, or any you would remove

from the existing model. Keep in mind the hotel's objective of understanding operating margin to inform its decisions about new hotel sites.

$($b$)$ How may 'operational data' held by organisations help them to build up an understanding of customer behaviour? Support your answer with examples.