Question

Suppose a colleague of yours estimated a regression model using 100,000 observations, and found that all the explanatory variables in the model were highly significant (at p values of less than 0.01). However, when calculating the marginal effects, the actual impact of many of the x variables on the y variable was very small in magnitude, suggesting the x variables do little to help predict y. How could this be possible (Hint, reference the formula for the standard error of your coefficient).

Answer 1

The significance of the variables is not decided by the magnitude of the coefficient only, rather the strandard deviation of the respective coefficient. The t-statistic is calculated as the [coefficient/se(coefficient)] under the null hypothesis that the concerned parameter is equal to zero. Since the coefficients of the variables are highly significant, the respective standard errors are also very small. The magntude of the coefficients are very small, which indicates that the the scale of those explanatory variables are very large, so that the overall contribution of the explanatory variables are meaningful.