each pair of numbersðx;yÞbe represented by a dot in a diagram with thex’s
on the horizontal axis, and we have the scatter diagram shown in Figure 8.1.
The dots do not fall perfectly on a straight line, but scatter around a line, very
typical for statistical relationships. However, a straight line seems to fit very
well. Generally, the 12 dots go from upper left to lower right, and we have a
negative association. As shown in Example 2.8, we obtained a Pearson’s cor-
relation coe‰cient ofr¼ 0 :946, indicating a very strong negative association.
TABLE 8.1
xyx^2 y^2 xy
112 63 12,544 3,969 7,056
111 66 12,321 4,356 7,326
107 72 11,449 5,184 7,704
119 52 14,161 2,704 6,188
92 75 8,464 5,625 6,900
80 118 6,400 13,924 9,440
81 120 6,561 14,400 9,720
84 114 7,056 12,996 9,576
118 42 13,924 1,764 4,956
106 72 11,236 5,184 7,632
103 90 10,609 8,100 9,270
94 91 8,836 8,281 8,5541,207 975 123,561 86,487 94,322
Figure 8.1 Graphical display for data in Example 8.1.286 CORRELATION AND REGRESSION