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best-fitting line .

F ITTING A L INE TO D ATA. 8. 6. 4. 2. –8. –6. –4. –2. 0. 2. 4. 6. –2. –4. –6. –8. There are several ways to find the best-fitting line for a given set of data points. In this lesson, you will use a graphical approach.

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best-fitting line .

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  1. FITTING A LINE TO DATA 8 6 4 2 –8 –6 –4 –2 0 2 4 6 –2 –4 –6 –8 There are several ways to find the best-fitting line for a given set of data points. In this lesson, you will use a graphical approach. Usually, there is no single line that passes through all the data points, so you try to find the line that best fits the data. This is called the best-fitting line. best-fitting line.

  2. 250 DISCUS THROWS Approximating a Best-Fitting Line 240 230 220 210 200 190 180 Distance (ft) 170 160 150 140 130 120 110 100 0 8 16 24 32 40 48 56 64 72 80 88 96 104 Years since 1900 The winning Olympic discus throws from 1908 to 1996 are plotted in the graph. Approximate the best-fitting line for these throws. Write an equation of your line.

  3. (96, 230) 250 Approximating a Best-Fitting Line 240 230 220 (8, 138) 210 (96, 230). 200 190 180 Distance (ft) 170 160 150 140 (8, 138) 130 120 110 100 0 8 16 24 32 40 48 56 64 72 80 88 96 104 Years since 1900 SOLUTION Find two points that lie on the best-fitting line, such as (8, 138) and (96, 230). Find the slope of the line through these points.

  4. (96, 230) 250 Approximating a Best-Fitting Line y2–y1 92 88 230–138 240 = 1.05 230–138 m = 92 88 1.05 = = = 96–8 x2–x1 230 96–8 220 210 200 190 180 Distance (ft) 170 160 150 140 (8, 138) 130 120 An equation of the best-fitting line isy = 1.05x + 129.6. 110 In most years, the winner of the discus throw was able to throw the discus farther than the previous winner. 100 0 8 16 24 32 40 48 56 64 72 80 88 96 104 Years since 1900 y = mx+b Write slope intercept form. Substitute 1.05 for m, 8 for x, 138 for y. 138= (1.05)(8) + b 138 = 8.4 + b y = mx+b Simplify. Solve for b. 129.6 =b

  5. DETERMINING THE CORRELATION OF X AND Y In this scatter plot, x and yhave a positive correlation, which means that the points can be approximated by a line with a positive slope.

  6. DETERMINING THE CORRELATION OF X AND Y In this scatter plot, x and y have a negative correlation, which means that the points can be approximated by a line with a negative slope.

  7. DETERMINING THE CORRELATION OF X AND Y In this scatter plot, x and y have relatively no correlation, which means that the points cannot be approximated by a line.

  8. TYPES OF CORRELATION DETERMINING THE CORRELATION OF X AND Y Positive Correlation Negative Correlation No Correlation

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