The hypothesis test for the population coefficient of determination can be a one- tail test or a two- tail test.

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The hypothesis test for the population coefficient of determination (R^2) typically involves testing the significance of the overall regression model rather than conducting a one-tail or two-tail test directly on R^2. The significance of R^2 is usually assessed through the F-test in the ANOVA table for the regression, which tests if the explained variance in the model is significantly greater than the unexplained variance, not through direct one-tail or two-tail tests on R^2 itself.

The Hypothesis Test for the Population Coefficient of Determination Can