The plot compares
unadjusted final exam marks in two courses [Bio3250
(Principles of Genetics) and Bio3900 (Principles of
Evolution)] for all persons who took both courses from the same
instructor in successive Fall and Winter semesters. These marks
are highly correlated: r2 = 0.51. The regression
line with a slope of r
= 0.7 uses 3250 marks (X) to predict performance
(Y) in the following semester.
Note that several broad trends
(1) No-one with an A in 3250 got less than a B in 3900,
(2) Most people with a B in 3250 get a B in 3900, and
(3) No-one who receives less than a C in 3250 receives better than a B in 3900.
Despite the high correlation, there is considerable scatter about the regression line. Notice that persons who got a B in 2250 got marks ranging from A ~ D in 3900, and those who got C have a range of B ~ D in 3900. That is, despite the high correlation, there is a wide range of variation in individual performance.
All text material © 2011 by Steven M. Carr