Question

A suburban hotel derives its gross income from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied.

Day     Income     Occupied
1     $1,452     23
2     1,361     47
3     1,426     21
4     1,470     39
5     1,456     37
6     1,430     29
7     1,354     23
8     1,442     44
9     1,394     45
10     1,459     16
11     1,399     30
12     1,458     42
13     1,537     54
14     1,425     27
15     1,445     34
16     1,439     15
17     1,348     19
18     1,450     38
19     1,431     44
20     1,446     47
21     1,485     43
22     1,405     38
23     1,461     51
24     1,490     61
25     1,426     39

Use a statistical software package to answer the following questions.
a. Does the breakfast revenue seem to increase as the number of occupied rooms increases? Draw a scatter diagram to support your conclusion.
b. Determine the coefficient of correlation between the two variables. Interpret the value.
c. Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the .10 significance level.
d. What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied?