A suburban hotel derives its revenue 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. The dataset is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and the number of rooms occupied. 1) Does the revenue seem to increase as the number of occupied rooms increases? Draw a scatter diagram to support your conclusion. 2) Determine the correlation coefficient between the two variables. Interpret the value. 3) Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the .10 significance level. 4) What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
A suburban hotel derives its revenue 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. The dataset is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and the number of rooms occupied. |
1) Does the revenue seem to increase as the number of occupied rooms increases? Draw a |
2) Determine the |
3) Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the .10 significance level. |
4) What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied? |
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The Cronch Café, located at the Gulf of Mexico, has an increase in business during
PART II TASKS: the summer vacation season. The owner hires a large number of servers as
1
Customer Amount of Tip ($) Amount of Bill ($) Diners
seasonal help. When he interviews a prospective server, he would like to provide
data on the amount a server can earn in tips. He believes that the amount of the bill
2
1
5.15
74.5
2
3
2
4.5
28.23
4
and the number of diners are both related to the amount of the tip. He gathered this
sample information.
4
3
1
10.65
1
4
2.4
19.82
3
6
5
28.62
3
1) Develop a multiple regression model with the amount of tips as the dependent
variable and the amount of the bill and the amount of diners as independent
7
4.25
24.83
2
12 points
8
7
0.5
6.25
variables. (5 points) Write out the regression equation. (4 points) How much does
another diner add to the amount of the tips? (3 points)
9
8
49.2
4.
10
43.26
3
2) Conduct a global test of hypothesis to determine if at least one of the independent 8 points
variables is significant. (4 points) What is your conclusion? (4 points)
11
10
4.65
62.23
1
12
11
5.6
84.81
1.
13
12
6
34.99
3
14
13
4
33.91
4
15
14
3.35
23.06
2
16
15
0.75
4.65
1
17
16
3.3
23.59
2
18
17
3.5
22.3
2
19
18
3.25
32
2
20
19
5.4
50.02
4
21
20
2.25
17.6
3
22
21
4.35
63.16
23
22
3
20.27
2
Task 1
Task 2
囲
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Customer
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10
9
43.26
3
2) Conduct a global test of hypothesis to determine if at least one of the independent 8 points
variables is significant. (4 points) What is your conclusion? (4 points)
11
10
4.65
62.23
1
12
11
5.6
84.81
1.
13
12
6
34.99
3
14
13
4
33.91
4
15
14
3.35
23.06
2
16
15
0.75
4.65
17
16
3.3
23.59
2
18
17
3.5
22.3
2
19
18
3.25
32
2
20
19
5.4
50.02
4
21
20
2.25
17.6
3
22
21
4.35
63.16
6
23
22
3
20.27
2
24
23
1.25
19.53
2
25
24
3.25
27.03
3
26
25
21.28
2
27
26
6.25
43.38
4
28
27
5.6
28.12
4
29
28
2.5
26.25
2
30
29
6.85
53.08
7
31
30
8.6
87.85
8
32
Task 1
Task 2
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