Regression using SPSS – A suburban hotel derives its gross income from its hotel and restaurant operations.

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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?

Answer

(A)

(B)
r = 0.44, there is a WEAK positive correlation.
(C)
df = n-2 = 25-2 = 23
α = 0.05
one-tailed critical value T = 1.319
Test statistic T = r*Sqrt[(n-2)/(1-r²)] = 0.44*Sqrt[(25-2)/(1-0.44²)] = 2.35
Conclusion: Since 2.35 > 1.319 we conclude that there is a positive relationship between the variables.
(D)
r² = 0.44² = 0.1936, so approximately 19% of the variation in revenue is explained by the variation in the number of rooms occupied.

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Regression using SPSS – A suburban hotel derives its gross income from its hotel and restaurant operations.

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