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    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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    Solution Summary

    #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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