Algebra II Recipe: Correlations and Best-Fitting Lines
By G Redden
A. Scatter Plots and Correlation
- scatter plot - a graph used to determine if there is a relationship between paired data.
- positive correlation - when "y" increases as "x" increases
- negative correlation - when "y" decreases as "x" increases
- no correlation - when the points show no linear relationship
B. Approximating Best-Fitting Lines (by hand)
- Draw a scatter plot of the data.
- Sketch a trend line - the line that most closely follows the pattern of the points. There should be as many points above the line as below the line.
- Choose two points on the line. These do NOT have to be original data points.
- Use the two points to write the equation of the line. This equation models the data and can be used to make predictions or estimations.
1.
1. Find the best-fitting line using the following data.
(0, 3.3)
(2, 6.3)
(2, 6.9)
(3, 7.2)
(3, 7.5)
(3, 7.8)
(4, 7.7)
(4, 8.1)
(5, 7.9)
(5, 8.6)
(6, 9.1)
(7, 9.4)
(7, 10.1)
(8, 9.8)
(9, 10.5)
(10, 10.8)
2.
2. The data pairs give the average speed of an airplane during the first 10 minutes of flight. Let x represent the number of minutes and y represent the speed in miles per hour. Find the best-fitting line for the data.
(1, 180)
(2, 250)
(3, 290)
(4, 310)
(5, 400)
(6, 420)
(7, 410)
(8, 490)
(9, 520)
(10, 510)
3.
3. The table gives the average heights of children for ages 1-10. Find the best-fitting line.
AGE (years) 1 2 3 4 5 6 7 8 9 10 HEIGHT (cm) 73 85 93 100 107 113 120 124 130 135
