12.6 Linear Correlation and Regression 829 Note that the numerator of the fraction used to determine m is identical to the numerator used to determine r. Therefore, if you have previously determined r, you do not need to repeat this calculation. Also, the denominator of the fraction used to determine m is identical to the radicand of the first square root in the denominator of the fraction used to determine r. Learning Catalytics Keyword: Angel-SOM-12.6 (See Preface for additional details.) Example 3 The Line of Best Fit a) Use the data in Example 1 to determine the equation of the line of best fit that relates the number of workers absent on an assembly line and the number of defective parts produced. b) Graph the equation of the line of best fit on a scatter diagram that illustrates the set of bivariate points. Solution a) In Example 1, we determined Σ − Σ Σ = n xy x y ( ) ( )( ) 520and Σ − Σ = n x x ( ) ( ) 161. 2 2 Thus, = Σ − Σ Σ Σ − Σ = ≈ m n xy x y n x x ( ) ( )( ) ( ) ( ) 520 161 3.23 2 2 Now we determine b. In Example 1, we determined = Σ = n x 6, 17, and Σ = y 106. = Σ − Σ ≈ − ≈ ≈ b y m x n ( ) 106 3.23(17) 6 51.09 6 8.52 Therefore, the equation of the line of best fit, with values rounded to the nearest hundredth, is y mx b y x 3.23 8.52 = + = + where x represents the number of workers absent and y represents the number of defective parts produced. b) To graph y x 3.23 8.52, = + we need to plot at least two points. We will plot three points and then draw the graph. = + = = + = = = + = = = + = y x x y x y x y 3.23 8.52 2 3.23(2) 8.52 14.98 4 3.23(4) 8.52 21.44 6 3.23(6) 8.52 27.90 x y 2 14.98 4 21.44 6 27.90 These three calculations indicate that if 2 assembly line workers are absent on the assembly line, the predicted number of defective parts produced is about 15. If 4 assembly line workers are absent, the predicted number of defective parts produced is about 21, and if 6 assembly line workers are absent, the predicted number of defective parts produced is about 28. Plot the three points (the three
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