10-1 Correlation 509 Interpreting Scatterplots Figure 10-2 shows four scatterplots with different characteristics. ■ Figure 10-2(a): Distinct straight-line, or linear, pattern. We say that there is a positive linear correlation between x and y, since as the x values increase, the corresponding y values also increase. ■ Figure 10-2(b): Distinct straight-line, or linear pattern. We say that there is a negative linear correlation between x and y, since as the x values increase, the corresponding y values decrease. ■ Figure 10-2(c): No distinct pattern, which suggests that there is no correlation between x and y. ■ Figure 10-2(d): Distinct pattern suggesting a correlation between x and y, but the pattern is not that of a straight line. FIGURE 10-1 Scatterplot from Table 10-1 (a) Positive correlation: r = 0.859 (b) Negative correlation: r = −0.971 (c) No correlation: r = 0.074 (d) Nonlinear relationship: r = 0.330 FIGURE 10-2 Scatterplots Measure the Strength of the Linear Correlation with r Because conclusions based on visual examinations of scatterplots are largely subjective, we need more objective measures. We use the linear correlation coefficient r, which is a number that measures the strength of the linear association between the two variables.
RkJQdWJsaXNoZXIy NjM5ODQ=