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    Correlation & Regression Analysis

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    Sample Number Assets ($ millions) Return (%)
    1 AARP 622.2 10.8
    2 Babson 160.4 11.3
    3 Compass 275.7 11.4
    4 Galaxy 433.2 9.1
    5 Keystone 437.9 9.2
    6 MFS Bond A 494.5 11.6
    7 Nichols 158.3 9.5
    8 T Rowe 681 8.2
    9 Thompston 241.3 6.8

    The table above contains data from 9 mutual funds -- total assets held by the fund and last year's return on the investment of the assets (cash).

    (1) Construct a scatter diagram -- I have to be sure I choose the correct dependent and independent variable. Think about these questions: Which variable influences the other? What is the direction of the relationship? Do assets influence the return or does the return influence the assets? What I choose as the "causing" variable will be X, what I choose as the variable being "caused" or influenced will be Y. Then I must discuss my diagram.

    (2) Compute the coefficients of correlation and determination and discuss what they mean.

    (3) Test the signficance of the sample correlation computed in #2.

    (4) Develop a regression equation. What return should I predict for $400M in assets? Is the regression equation I developed meaningful? Why or why not?

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    Solution Summary

    The solution provides step by step method for the calculation of test statistic for significance of correlation coefficient and regression analysis. Formula for the calculation and Interpretations of the results are also included.