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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. 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. –8 8 6 4 2 –2 –4 –6 0246–2–4–6–8 F ITTING A L INE TO D ATA

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Approximating a Best-Fitting Line D ISCUS T HROWS Years since 1900 Distance (ft) 081624324048566472808896104 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 Write an equation of your line. The winning Olympic discus throws from 1908 to 1996 are plotted in the graph. Approximate the best-fitting line for these throws.

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Approximating a Best-Fitting Line Years since 1900 Distance (ft) 081624324048566472808896104 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 S OLUTION 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. ( 96, 230 ). (96, 230) ( 8, 138 )

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92 88 = 1.05 Years since 1900 Distance (ft) 081624324048566472808896104 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 (96, 230) (8, 138) y = m x + b 230 – 138 96 – 8 = 129.6 = b Write slope intercept form. Substitute 1.05 for m, 8 for x, 138 for y. Simplify. Solve for b. An equation of the best-fitting line is y = 1.05 x + 129.6. 138 = (1.05) (8) + b y = m x + b 138 = 8.4 + b y2 – y1y2 – y1 x2 – x1x2 – x1 m = In most years, the winner of the discus throw was able to throw the discus farther than the previous winner. Approximating a Best-Fitting Line 230 – 138 96 – 8 = 92 88 = 1.05

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D ETERMINING THE C ORRELATION OF X AND Y In this scatter plot, x and y have a positive correlation, which means that the points can be approximated by a line with a positive slope.

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D ETERMINING THE C ORRELATION 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.

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D ETERMINING THE C ORRELATION 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.

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D ETERMINING THE C ORRELATION OF X AND Y T YPES OF C ORRELATION Positive Correlation No CorrelationNegative Correlation

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