2-4 Scatterplots, Correlation, and Regression 79 The regression equation yn = b 0 + b1x where b0 is the y-intercept of the line and b1 is the slope of the line. This equation algebraically describes the regression line. Section 10-2 gives a good reason for using the format of yn = b 0 + b1x instead of the format of y = mx + b. Section 10-2 also provides formulas that could be used to identify the values of the y-intercept b0 and the slope b1, but those values are usually found by using statistics software or a suitable calculator. Regression Line EXAMPLE 6 Example 5 included a scatterplot of the 40 pairs of shoe print lengths and heights from Data Set 9 “Foot and Height” in Appendix B. Figure 2-19 is that same scatterplot with the graph of the regression line included. Also shown is the Statdisk display from the 40 pairs of data. From the Statdisk display, we see that the general form of the regression equation has a y-intercept of b0 = 80.9 (rounded) and slope b1 = 3.22 (rounded), so the equation of the regression line shown in Figure 2-19 is yn = 80.9 + 3.22x. It might be helpful to express that equation more clearly by using the names of the variables: Height = 80.9 + 3.22 1Shoe Print Length2 Note that the equation shows the y-intercept of 80.9 that does not appear on the vertical scale in the graph. The leftmost vertical scale in Figure 2-19 is not the actual y-axis that passes through 0 on the x-axis. If the graph were extended to the left, the regression line would intercept the actual y-axis at the height of y = 80.9 cm. FIGURE 2-19 Regression Line Statdisk Statistical Literacy and Critical Thinking 1.Linear Correlation In this section we use r to denote the value of the linear correlation coefficient. Why do we refer to this correlation coefficient as being linear? 2. Causation A study has shown that there is a correlation between body weight and blood pressure. Higher body weights are associated with higher blood pressure levels. Can we conclude that gaining weight is a cause of increased blood pressure? 2-4 Basic Skills and Concepts
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