In: Statistics and Probability
Using Excel
Data in Travel file shows the average number of rooms in a variety of U.S cities and the average room rate and the average amount spent on entertainment. A company that run events for hotel residents wants to predict the amount spent on entertainment based on room rate and number of rooms.
Run the regression analysis. Are the coefficients statistically significant? Do we need to drop one of these variable? Which variable? Interpret the slope of the estimated regression equation?
Develop the least squares estimated regression equation. The average room rate in Chicago is $128, predict the entertainment expense per day for Chicago.
City | Entertainment ($) | Room Rate ($) | # of rooms |
Boston | 160 | 149 | 63 |
Denver | 104 | 98 | 500 |
Nashville | 100 | 90 | 460 |
New Orleans | 141 | 111 | 300 |
Phoenix | 101 | 91 | 650 |
San Diego | 121 | 103 | 350 |
San Francisco | 167 | 134 | 200 |
San Jose | 141 | 91 | 230 |
Tampa | 97 | 81 | 126 |
We use Minitab to solve this question-
The required first regression equation is,
Entertainment ($) = 46.5 + 0.868 Room Rate ($) - 0.0378 No of
Rooms
The pvalue corresponding to variable No of Rooms is 0.285 > 0.05
therefore it is not statistically significant. We drop variable No
of Rooms and fit new regression model as,
Entertainment ($) = 17.6 + 1.027 Room Rate ($)
Now, At room rate $128,
Entertainment ($) = 17.6 + 1.027 Room Rate ($)
Entertainment ($) = 17.6 + 1.027 * $ 128
Entertainment ($) = 149
predicted the entertainment expense per day for Chicago is $
149