each pair of numbersðx;yÞbe represented by a dot in a diagram with thex’s
on the horizontal axis; we have the scatter diagram shown in Figure 8.2. Again
the dots do not fall perfectly on a straight line, but scatter around a line, very
typical for statistical relationships. In this example, a straight line still seems
to fit, too; however, the dots spread more and cluster less around the line,
indicating a weaker association. Generally, the 15 dots go from lower left to
upper right, and we have a positive association. As shown in Example 2.9, we
obtained a Pearson’s correlation coe‰cient ofr¼ 0 :566, indicating a moder-
ately positive association, confirming the observation from the graph.
Applying the formulas, we obtain estimates for the slope and intercept as
follows:
b 1 ¼146 ; 260 ð 984 Þð 2193 Þ= 15
67 ; 954 ð 984 Þ^2 = 15
¼ 0 : 71x¼984
15
¼ 65 : 6
y¼2193
15
¼ 146 : 2
TABLE 8.2
xyx^2 y^2 xy
42 130 1,764 16,900 5,460
46 115 2,116 13,225 5,290
42 148 1,764 21,904 6,216
71 100 5,041 10,000 7,100
80 156 6,400 24,336 12,480
74 162 5,476 26,224 11,988
70 151 4,900 22,801 10,570
80 156 6,400 24,336 12,480
85 162 7,225 26,224 13,770
72 158 5,184 24,964 11,376
64 155 4,096 24,025 9,920
81 160 6,561 25,600 12,960
41 125 1,681 15,625 5,125
61 150 3,721 22,500 9,150
75 165 5,625 27,225 12,375984 2,193 67,954 325,889 146,260
288 CORRELATION AND REGRESSION