Question

17. How is the following dilemma explained: ‘There are insignificant estimated coefficients of the parameters in the equation, yet an F-test yields a robust result.’

Answer 1

One conclusion we can draw from this is that when too many variables are included in a model they can mask the truly significant ones. The first sign of this is the highly significant overall F statistic accompanied by not-so-significant t-tests for the individual coefficients. (Even when some of the variables are individually significant, this does not automatically mean the others are not. That's one of the basic defects of stepwise regression strategies: they fall victim to this masking problem.)

Even if you had no multicollinearity, you can still get non-significant predictors and an overall significant model if two or more individual predictors are close to significant and thus collectively, the overall prediction passes the threshold of statistical significance.