We expect students who do well within a course to also do well on the final exam. Gary Smith of Ponoma College reviewed the exam results of 346 students who took his statistics course over a period of 10 years. The line of least squares to make the prediction of the final exam score based on the intra score is = 46.6 + 0.41x. Octavio scored 10 points above the class average at the intra. By how many points should he be above average on the final exam? (Hint: what is the expected final exam mark for a mark within x?)

This is an example of the phenomenon of regression to the mean, a phenomenon which gave its name to regression: students who do well on the intra will, on average, do less well on the final, but will still remain above the group average.