Introduction to Probability and Statistics for Engineers and Scientists

38 Chapter 2:Descriptive Statistics

r = –.50 r = 0

r = –.90

FIGURE 2.14 Sample correlation coefficients.

The sign ofrgives the direction of the relation. It is positive when the linear relation is
such that smalleryvalues tend to go with smallerxvalues and largeryvalues with largerx
values (and so a straight line approximation points upward), and it is negative when larger
yvalues tend to go with smallerxvalues and smalleryvalues with largerxvalues (and so
a straight line approximation points downward). Figure 2.14 displays scatter diagrams for
data sets with various values ofr.

EXAMPLE 2.6a Find the sample correlation coefficient for the data presented in Table 2.8.

SOLUTION A computation gives the solution

r=.4189

thus indicating a relatively weak positive correlation between the daily temperature and
the number of defective items produced that day. ■