Which test is appropriate for determining whether a regression coefficient differs significantly from zero?

The correct test for determining whether a regression coefficient differs significantly from zero is the t-test. In the context of regression analysis, a t-test is used to assess the null hypothesis that the coefficient (slope) of an independent variable is equal to zero. If the coefficient is statistically significantly different from zero, this suggests that there is an association between the independent variable and the dependent variable in the regression model.

In regression, each regression coefficient is analyzed individually to determine if it contributes meaningfully to the prediction of the outcome variable. By applying a t-test, researchers can gauge the strength and direction of the relationship, allowing for conclusions about whether the independent variable should be retained in the model.

Other tests presented in the question serve different purposes. ANOVA is typically used to compare means across multiple groups rather than for examining individual regression coefficients. The Friedman Test is a non-parametric alternative to repeated measures ANOVA, focused on ranks rather than assessing relationships in regression. The Kruskal-Wallis Test is also a non-parametric method for comparing more than two groups based on their ranks without addressing regression coefficients directly. Therefore, a t-test is the definitive choice for evaluating the significance of individual regression coefficients.