A sample of n = 15 pairs of X and Y scores produces a Pearson correlation of r =

Question

A sample of n = 15 pairs of X and Y scores produces a Pearson correlation of r = 0.45 with SS_y = 90. a. Find how much of the Y variability would be predicted by the regression equation by calculating the SS_regression. b. Find how much of the variability in Y would not be predicted by the regression equation by calculating the SS_residual. We want to know if the regression equation predicts a significant portion of the variability for the Y scores by testing the significance of the regression. a. State the null hypothesis b. Identify the critical region c. Calculate the test statistic (must calculate the MS_regression and MS_residual to calculate the F statistic) d. State your conclusion

Explanation / Answer

a) Given,

r = 0.45

So,

Coefficient of determination = 0.452 = 0.2025

Hence,

20.25% of the variation in y values can be explained by independent variable.

Hence,

SSRegression = 0.2025 * SSY = 0.2025*90 = 18.225

b) SSResidual = SSY - SSRegression = 90 - 18.225 = 71.775

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