824 CHAPTER 12 Statistics Number of Defective Parts 5 0 1 2 3 4 5 6 10 15 20 25 30 x y Number of Workers Absent Figure 12.40 The figure shows that, generally, the more workers that are absent, the more defective parts are produced. In Fig. 12.41, we show some scatter diagrams and indicate the corresponding strength of correlation between the quantities on the horizontal and vertical axes. Earlier, we mentioned that r will always be a value between 1− and 1 inclusive. A value of r 1 = is obtained only when every point of the bivariate data on a scatter diagram lies in a straight line and the line is increasing from left to right (Fig. 12.41(a)). In other words, the line has a positive slope, as discussed in Section 6.6. A value of r 1 = − will be obtained only when every point of the bivariate data on a scatter diagram lies in a straight line and the line is decreasing from left to right. (Fig. 12.41(e)). In other words, the line has a negative slope. The value of r is a measure of how far a set of points varies from a straight line. The greater the spread, the weaker the correlation and the closer the value of r is to 0. Fig. 12.41 shows that the more the points diverge from a straight line, the weaker the correlation becomes. y (a) r = 1; strongest positive correlation x y (b) r > 0; strong positive correlation x y (c) r > 0; moderate to weak positive correlation x y (d) No correlation x x y (e) r = –1; strongest negative correlation x y (f) r < 0; strong negative correlation x y (g) r < 0; moderate to weak negative correlation x y (h) No correlation Figure 12.41
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