1. 2.5 Correlation and Best-Fitting Lines
Algebra 2

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

3. 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

4. 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

5. 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.

6. 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

7. Example
The data pairs give the number of U.S. births from 1990 to 1997, where x is years since 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

8. 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. ( ), (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