Exercise 11.6:
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A multiple linear regression analysis involving 10 predictors. The overall F-
test is strongly significant but none of the 10 regression coefficients are
significant.

The overall F-test tests the hypothesis
  H0: beta1=1, beta2=0, ..., beta10=10
whereas the individual t-tests each test a hypothesis about a single regression
coefficient H0: beta_k=0, in the presence of the other 9 variables in the model.
When the predictors are collinear, removing a single predictor will affect the
regression coefficients of all remaining predictors. Therefore, the 10 tests for
individual regression coefficients say nothing about the combined significance of
several regression coefficients. Specifically, if the 10 predictors explain 
more or less the same part of the variation of the outcome, it is possible to 
remove one (or several) predictor(s) without substantially affecting the model 
fit because the remaining predictors can compensate.

In the situation discussed, the outcome being the score at the final exam, and
the predictors the scores on quizzes during the course, a strong collinearity is
to be expected. Students tend to do generally well or less well on the quizzes, 
and the former category of students typically do well on the final exam.