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    In 2009, the New York Yankees won 103 baseball
    games during the regular season. The table on the next
    page lists the number of victories (W), the earnedrun-
    average (ERA), and the batting average (AVG)
    of each team in the American League. The ERA is
    one measure of the effectiveness of the pitching staff,
    and a lower number is better. The batting average
    is one measure of effectiveness of the hitters, and a
    higher number is better.

    (a) Develop a regression model that could be used to
    predict the number of victories based on the ERA.
    (b) Develop a regression model that could be used to
    predict the number of victories based on the batting
    (c) Which of the two models is better for predicting
    the number of victories?
    (d) Develop a multiple regression model that includes
    both ERA and batting average. How does
    this compare to the previous models?

    New York Yankees 103 4.26 0.283
    Los Angeles Angels 97 4.45 0.285
    Boston Red Sox 95 4.35 0.270
    Minnesota Twins 87 4.50 0.274
    Texas Rangers 87 4.38 0.260
    Detroit Tigers 86 4.29 0.260
    Seattle Mariners 85 3.87 0.258
    Tampa Bay Rays 84 4.33 0.263
    Chicago White Sox 79 4.14 0.258
    Toronto Blue Jays 75 4.47 0.266
    Oakland Athletics 75 4.26 0.262
    Cleveland Indians 65 5.06 0.264
    Kansas City Royals 65 4.83 0.259
    Baltimore Orioles 64 5.15 0.268

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    Solution Summary

    This solution is comprised of a detailed explanation of regression analysis. In this solution, step-by-step explanation of this complicated topic provides students with a clear perspective of standard normal distribution to find the probability.