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Explain why a multiple regression analysis reported an F statistic with a p < 0.05 but...

Explain why a multiple regression analysis reported an F statistic with a p < 0.05 but none of the individual coefficients were significant.

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Solution: In multiple regression analyses, we can see the results are statistically significant using the F-statistic but none of the individual coefficients are significant. The reason for such results is that the F-test tests the overall significance of the model and individual t-test tests the significance of the individual significance of the coefficient. Therefore, F-test determines that the coefficients are jointly not all equal to zero, while the individual t-tests determine that all of them are individually not equal to zero.

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