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How do I find the equation of a line of best fit for a scatter plot? How do I find and interpret the correlation coefficient, r?

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S.ID.8 Interpreting Correlation Example 1 Describe and estimate correlation coefficients Describe the data as having a positive correlation, a negative correlation, or approximately no correlation. Tell whether the correlation coefficient for the data is closest to or a. Solution a.The scatter plot shows a strong _________ correlation. negative So, the best estimate given is r = ____.

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So, r is between ___ and ___, but not too close to either one. The best estimate given is r = _____. S.ID.8 Interpreting Correlation Example 1 Describe and estimate correlation coefficients Describe the data as having a positive correlation, a negative correlation, or approximately no correlation. Tell whether the correlation coefficient for the data is closest to or b. Solution b.The scatter plot shows a weak _________ correlation. positive

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S.ID.8 Interpreting Correlation Checkpoint. For the scatter plot, (a) tell whether the data has a positive correlation, a negative correlation, or approximately no correlation, and (b) tell whether the correlation coefficient for the data is closest to or 1. a.positive correlation b.1 1.

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S.ID.8 Interpreting Correlation Checkpoint. For the scatter plot, (a) tell whether the data has a positive correlation, a negative correlation, or approximately no correlation, and (b) tell whether the correlation coefficient for the data is closest to or 1. a.approximately no correlation b.0 2.

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S.ID.6 Draw Scatter Plots and Best-Fitting Lines Example 2 Approximate the best-fitting line The table below gives the number of people y who attended each of the first seven football games x of the season. Approximate the best- fitting line for the data. x1234567 y722763772826815857897 0 1 2 3 4 5 6 7 650 700 750 800 850 900 1.Draw a __________. scatter plot 2.Sketch a best-fitting line. 3.Choose two points on the line. For the scatter plot shown, you might choose (1, ___) and (3, ___). 722 772 4.Write an equation of the line. The line passes through the two points has a slope of:

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S.ID.6 Draw Scatter Plots and Best-Fitting Lines Example 2 Approximate the best-fitting line The table below gives the number of people y who attended each of the first seven football games x of the season. Approximate the best- fitting line for the data. x1234567 y722763772826815857897 0 1 2 3 4 5 6 7 650 700 750 800 850 900 Use the slope-intercept form to write the equation. Choose a point from the table to substitute in for x and y. m = 25 ; Use (1, 722). 722 = 25(1) + b 722 = 25 + b 697 = b An approximation of the best-fitting line is

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S.ID.6 Draw Scatter Plots and Best-Fitting Lines Example 2 Approximate the best-fitting line The table below gives the number of people y who attended each of the first seven football games x of the season. Approximate the best- fitting line for the data. x1234567 y722763772826815857897 0 1 2 3 4 5 6 7 650 700 750 800 850 900 You can enter the data in your calculator to get the equation for the line of best fit also. Enter the x data in L1 and the y data in L2. Run 2-VAR STATS. a = slope and b = y-int. An approximation of the best-fitting line from the calculator is

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S.ID.8 Draw Scatter Plots and Best-Fitting Lines Example 2 Approximate the best-fitting line The table below gives the number of people y who attended each of the first seven football games x of the season. Approximate the best- fitting line for the data. x1234567 y722763772826815857897 0 1 2 3 4 5 6 7 650 700 750 800 850 900 In addition, the correlation coefficient, r, can be found on the calculator. Scroll down past a and b, and you will find that the correlation coefficient for this example is r = 0.976. This indicates that the line y = 27x + 699.4 fits the data well since r is close to 1.

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S.ID.6 & 8 Draw Scatter Plots and Best-Fitting Lines Checkpoint. Complete the following exercise. 3.The table gives the average class score y on each chapter test for the first six chapters x of the textbook. x123456 y848386888790 0 1 2 3 4 5 6 7 82 84 86 88 90 92 a.Approximate the best-fitting line for the data by hand. So, the equation describing this data is y = 4/3x + 82. y = mx + b 86 = 4/3(3) + b 86 = 4 + b 82 = b

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S.ID.6 & 8 Draw Scatter Plots and Best-Fitting Lines Checkpoint. Complete the following exercise. 3.The table gives the average class score y on each chapter test for the first six chapters x of the textbook. x123456 y848386888790 0 1 2 3 4 5 6 7 82 84 86 88 90 92 b.Approximate the best-fitting line using your calculator. c.Find the correlation coefficient, r. From the calculator, a = 1.26 and b = 81.93. So, the equation describing this data is y = 1.26x + 81.93. From the calculator, r = 0.91, which suggests that the equation fits the data well since r is close to 1.

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S.ID.6 Draw Scatter Plots and Best-Fitting Lines Checkpoint. Complete the following exercise. 3.The table gives the average class score y on each chapter test for the first six chapters x of the textbook. x123456 y848386888790 0 1 2 3 4 5 6 7 82 84 86 88 90 92 d. Use your equation from part (a) to predict the average class score on the chapter 9 test. The average class score on the chapter 9 test is predicted to be a 94.

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