Regression analysis

37. A regional commuter airline selected a random sample of 25 flights and found that the
correlation between the number of passengers and the total weight, in pounds, of luggage
stored in the luggage compartment is 0.94. Using the .05 significance level, can we
conclude that there is a positive association between the two variables?

Ex.40

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.

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?

Day Income Occupied
1 $1,452 23
2 1,362 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

Mike Wilde is president of the teachers' union for Otsego School District. In preparing
for upcoming negotiations, he would like to investigate the salary structure of classroom
teachers in the district. He believes there are three factors that affect a teacher's salary:
years of experience, a rating of teaching effectiveness given by the principal, and whether
the teacher has a master's degree. A random sample of 20 teachers resulted in the following
data.

Salary Years of Experience Principles Rating Masters's Degree
($ thoudands
Y X₁ X₂ X₃
31.1 8 35 0
33.6 5 43 0
29.3 2 51 1
43 15 60 1
38.6 11 73 0
45 14 80 1
42 9 76 0
36.8 7 54 1
48.6 22 55 1
31.7 3 90 1
25.7 1 30 0
30.6 5 44 0
51.8 23 84 1
46.7 17 76 0
38.4 12 68 1
33.6 14 25 0
41.8 8 90 1
30.7 4 62 0
32.8 2 80 1
42.8 8 70 0

1=yes 2=no
a. Develop a correlation matrix. Which independent variable has the strongest correlation
with the dependent variable? Does it appear there will be any problems with
multicollinearity?
b. Determine the regression equation. What salary would you estimate for a teacher with
five years' experience, a rating by the principal of 60, and no master's degree?