12.6 Linear Correlation and Regression 831 b) We evaluate y x 18.09 263.00 = − + at x 5. = y x y 18.09 263.00 18.09(5) 263.00 172.55 = − + = − + = Thus, after 5 hr, about 173 mg of the drug remains in the average person’s bloodstream. 7 Now try Exercise 35 TECHNOLOGY TIP We can use Microsoft EXCEL, the Texas Instruments TI-84 Plus graphing calculator, and StatCrunch to determine the correlation coefficient, r, and the equation of the line of best fit. Below we use the data from Example 1, where x represents the number of workers absent and y represents the number of defective parts for 6 selected days. Excel Begin by reading the Technology Tip on page 790. The instructions for determining the correlation coefficient and equation of the line of best fit are similar to the instructions given on page 790. In column A, rows 1 through 6, enter the 6 values representing the number of workers absent. In column B, rows 1 through 6, enter the 6 values that represent the number of defective parts. In general, the items listed on the horizontal axis in the scatter diagram (the independent variable if there is one) are placed in column A and the items listed on the vertical axis are placed in column B. Then select the following: Insert Function Statistical > …> Then to determine the value of the correlation coefficient, select CORREL and click OK . Excel will then generate a gray box and ask you for information about your data. In the box to the right of Array1 , type in A1:A6, and in the box to the right of Array2 , type in B1:B6. Then at the bottom of the box you will see Formula results 921927852 . , = which is the correlation coefficient. If you then wish to determine the equation of the line of best fit, press CANCEL on the bottom of the gray box. Then select Insert Function Statistical SLOPE OK > …> > > Excel will then generate a gray box. In the box to the right of Known_y’s , type in B1:B6. In the box to the right of Known_x’s , type in A1:A6. At that point, at the bottom of the box you will see Formula results 3 229813665 . , = which is the slope of the equation of the line of best fit. To determine the y-intercept, press CANCEL to remove the gray box. Then select Insert Function Statistical INTERCEPT OK > …> …> > Excel will then generate a gray box. In the box to the right of Known_y’s, type in B1:B6. In the box to the right of Known_x’s, type in A1:A6. At that point, at the bottom of the box you will see Formula results 8 51552795 . , = which is the y-coordinate of the y-intercept of the equation of the line of best fit. TI-84 Plus Graphing Calculators First, press 2nd CATALOG. Use the down arrow key until the indicator is pointing at DiagnosticOn. Press ENTER twice. This will enable the calculator to display the correlation coefficient and the line of best fit at the same time. Next, press STAT. Then select Edit . If you have any data in L1 or L2 , delete the data by going to L1 and pressing CLEAR and then ENTER. Follow a similar procedure to clear column L2 . Now enter the 6 pieces of data representing the number of workers absent in column L1 and enter the 6 pieces of data representing the number of defective parts in L2 . Then press STAT and highlight CALC . At this point, − 1:1 Var Stats should be highlighted. Scroll down to highlight
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