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**: r^{2} = 0.51. The **regression
line **with a slope of r
= 0.7 uses 3250 marks (X) to predict performance
in 3900
(Y) in the following semester.

Note that several broad trends
are apparent:

(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