# Regression analysis

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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?

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#The solution provides step by step method for the calculation of regression models . Formula for the calculation and Interpretations of the results are also included.

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