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

Approximating a Best-Fitting Line D ISCUS T HROWS Years since 1900 Distance (ft) 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.

Approximating a Best-Fitting Line Years since 1900 Distance (ft) 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 )

92 88 = 1.05 Years since 1900 Distance (ft) (96, 230) (8, 138) y = m x + b 230 – – 8 = = 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 = (1.05) (8) + b y = m x + b 138 = 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 – – 8 = = 1.05

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.

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.

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.

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