For some reason, students often have trouble interpreting confidence intervals correctly. Suppose they're presented with an OLS estimate of 1.1 for a regression coefficient, and an associated 95% confidence interval of [0.9,1.3]. Unfortunately, you sometimes see interpretations along the following lines:
- There's a 95% probability that the true value of the regression coefficient lies in the interval [0.9,1.3].
- This interval includes the true value of the regression coefficient 95% of the time.
So, what's wrong with these statements?