Calculating the correlation and testing a correlation coefficient's significance
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

1452

23

2

1361

47

3

1426

21

4

1470

39

5

1456

37

6

1430

29

7

1354

23

8

1442

44

9

1394

45

10

1459

16

11

1399

30

12

1458

42

13

1537

54

14

1425

27

15

1445

34

16

1439

15

17

1348

19

18

1450

38

19

1431

44

20

1446

47

21

1485

43

22

1405

38

23

1461

51

24

1490

61

25

1426

39

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