What determines whether a coefficient estimate is statistically significant?

Question

BlackTom AI · Accepted Answer

Question: What determines whether a coefficient estimate is statistically significant?

Option 1: 'Adjusted R Square.' Adjusted R-squared measures the proportion of variance explained by the model, adjusted for the number of predictors. It reflects model fit, not the individual significance of a single coefficient, so it does not determine whether a particular coefficient estimate is statistically significant.

Option 2: 'The magnitude of the coefficient.' The size of the coefficient tells you the practical or economic impact of a unit change in the predictor, but statistical significance depends on uncertainty around the estimate (standard error) and the corresponding p-value. A large magnitude can still be not statistically significant if the estimate is imprecise.

Option 3: 'R Square.' R-squared is a general measure of how much of the outcome variance is explained by the model. Like adjusted R-squared, it pertains to overall model fit rather than the significance of an individual coefficient, so it does not determine significance of a single parameter.

Option 4: 'P-value of the t-stat.' This is the correct concept: the statistical significance of a specific coefficient is assessed by the t-statistic, which is the ratio of the coefficient estimate to its standard error. The p-value from this t-test indicates whether we can reject the null hypothesis that the coefficient equals zero at a given significance level.

Option 5: 'P-value of the F-test.' The F-test p-value assesses whether the model (as a whole) provides a better fit than a model with no predictors, i.e., overall significance, not the significance of an individual coefficient. While related to model validity, it does not determine the significance of a single coefficient.

What determines whether a coefficient estimate is statistically significant?单项选择题

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