830 CHAPTER 12 Statistics In Example 3, the line of best fit intersects the y-axis at 8.52, the value we determined for the y b -intercept, , in part (a). black points in Fig. 12.44) and then draw a straight line through the three points. The scatter diagram and graph of the equation of the line of best fit are plotted in Fig. 12.44. Number of Defective Parts 5 0 1 2 3 4 5 6 10 15 20 25 30 x y Number of Workers Absent Figure 12.44 7 Now try Exercise 27 Correlation and Regression Example 4 Line of Best Fit for Example 2 a) Determine the equation of the line of best fit between the time elapsed and the amount of drug remaining in a person’s bloodstream in Example 2. b) If the average person is given 300 mg of the drug, how much will remain in the person’s bloodstream after 5 hr? Solution a) From the scatter diagram, we see that the slope of the line of best fit, m, will be negative. In Example 2, we determined that Σ − Σ Σ = − n xy x y ( ) ( )( ) 14,925 and that Σ − Σ = n x x ( ) ( ) 825. 2 2 Thus, = Σ − Σ Σ Σ − Σ = − ≈ − m n xy x y n x x ( ) ( )( ) ( ) ( ) 14,925 825 18.09 2 2 From Example 2, = Σ = n x 10, 55, and Σ = y 1635. = Σ − Σ ≈ − − ≈ b y m x n 1635 ( 18.09)(55) 10 263.00 Thus, the equation of the line of best fit, with values rounded to the nearest hundredth, is = + = − + y mx b y x 18.09 263.00 where x is the elapsed time and y is the amount of drug remaining.
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