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    Test for Regression Coefficient using Correlation Coefficient

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    Use a simple regression model to test the null hypothesis against the alternative
    Ho: Beta1 = 0
    H1: Beta1 Does NOT = 0

    with alpha = 0.05 , given the following regression statistics:

    a. The sample size is 35, SST = 100,000, and the correlation between X and Y is 0.46.
    b. The sample size is 61, SST = 123,000, and the correlation between X and Y is 0.65.
    c. The sample size is 25, SST = 128,000, and the correlation between X and Y is 0.69.

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    https://brainmass.com/statistics/regression-analysis/test-regression-coefficient-using-correlation-coefficient-591423

    Solution Preview

    Please see the attachment for solution.

    Here we need to test the null hypothesis H0: B1 = 0 against the alternative hypothesis .H1: B1 does not equal 0.
    The test statistic is
    F = MSR/MSE = SSR/s^2
    The decision rule is: Reject H0 if F >= F(1,n-2,infinity)
    We have the results
    R^2 = r^2, R^2 = SSR/SST = 1 - SSE/SST, and s^2 = SSE/(n-2) .
    a) Given that,
    n =35, SST = 100,000, r = 0.46
    Now,
    R^2 = (0.46)^2 = 0.2116.
    Substituting this result in R^2 = SSR/SST we get
    0.2116 = SSR/100,000
    That is, ...

    Solution Summary

    The solution illustrates the application of correlation coefficient in the test for significance of the regression coefficient.

    $2.19

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