2.5 Correlation and Best-Fitting Lines Algebra 2

Scatter Plots and Correlation Scatter Plot- a graph used to determine whether there is a relationship between paired data Positive correlation-the y-value tends to increase as the x-value increases Negative correlation- the y-value tends to decrease as the x-value increases Relatively no correlation- shows no linear pattern

Example Graph the data points (6, 200), (6, 325), (9, 299), (11, 500), (11, 675), (12.5, 720), (17, 780), (18.5, 750) and describe the correlation

Lines of Best-Fit Carefully graph the data Sketch the line that appears to follow most closely the pattern given by the data Choose two points on that line, and estimate their coordinates. Find the equation on the line

Example The data pairs give the average speed of an airplane during the first 10 minutes of a flight, with x in minutes and y in miles per hour. (1, 180), (2, 250), (3, 290), (4, 310), (5, 400), (6, 420), (7, 410), (8, 490), (9, 520), (10, 510) Describe the correlation shown. Approximate the best-fitting line for the data.

Example Graph the data. (5, 6000), (7, 5200), (10, 5100), (12, 5000), (16, 4100), (20, 4100), (24, 3800), (26, 3300), (30, 2900), (34, 2100), (36, 2200) Describe the correlation shown Estimate the line of best-fit for the data

Example The data pairs give the number of U.S. births from 1990 to 1997, where x is years since 1990 and y is in thousands. (0, 4158), (1, 4111), (2, 4065), (3, 4000), (4, 3953), (5, 3900), (6, 3891), (7, 3895) Approximate the line of best-fit Use the fitted line to estimate the number of births in the year 2000

Example The data pairs give the U.S. production of beef from 1990 to 1997, where x is years since 1990 and y is billions of pounds. (0 22.7), (1, 22.9), (2, 23.1), (3, 23.0), (4, 24.4), (5, 25.2), (6, 25.5), (7, 25.5) Approximate the line of best-fit Use the fitted line to estimate the beef production in the year 2000