Line of Best Fit

• ## Line of Best Fit

Grade: 6th to 8th, High School

This activity allows the user to enter a set of data, plot the data on a coordinate grid, and determine the equation for a line of best fit.

This interactive is optimized for your desktop and tablet.

### Instructions

• Plot points by clicking anywhere on the grid, or plot a set of points by entering a pair of coordinates in the text box and clicking Add Point
• Check the Remove Points box and click on any point to remove it. You can also click‑and‑drag any point to change its location.
• When you check the box for Show Guess, a purple line will appear on the grid. Drag the purple dots to approximate a line of best fit visually. An equation of this line will appear to the right. A slope and y-intercept can also be entered to change the line of best fit.
• When you check the box for Show Line of Best Fit, the area least-squares regression line will be displayed. An equation of this line and the correlation coefficient (r) will appear.
• The grid can be zoomed in and out as more points are added. Use the + and Magnifying Glass to zoom.
• To see a different portion of the grid, highlight the Move Graph box and use the mouse to drag the graph around.
• You can reset the original parameters for the graph or use the Zoom to Fit box to have the graph automatically select parameters that will show all your points optimally.

### Exploration

The data below shows the points scored and minutes played by the six "starters" for the Los Angeles Lakers during the 2004–05 season. (For this investigation, a "starter" is any player who averaged more than 20 minutes per game.)

Plot points scored along the horizontal axis and minutes along the vertical axis.

 PLAYER Points Minutes Kobe Bryant 1819 2689 Caron Butler 1195 2746 Chucky Atkins 1115 2903 Lamar Odom 975 2320 Chris Mihm 735 1870 Jumaine Jones 577 1830
 Enter 1819,2689 1195,2746 1115,2903 975,2320 735,1870 577,1830

Check the Show Line of Best Fit box to see a linear approximation of this data. The correlation coefficient (r) indicates how well the line approximates the data. If |r| = 1, the line is a perfect fit to the data; if |r| = 0, the line does not fit the data at all. In general, the closer |r| is to 1, the better the fit.

• What is the correlation coefficient (r) for this set of data?
• Remove the data for Kobe Bryant. How does this change the regression equation and r value?
• Replace the data for Kobe Bryant, and remove the data for another player. Repeat this process for each player in the list. For which player does the removal of data have the greatest impact on the regression equation and r value? What does the change indicate?
• Can you explain the changes that occurred when data was removed?

You can conduct similar investigations for other sports by looking at the statistics for Major League Baseball (MLB), National Football League (NFL), Women's National Basketball Association (WNBA), Major League Soccer (MLS), or other sports that interest you.

### Objectives and Standards

NCTM Standards and Expectations
• Probability / Data Analysis and Statistics
• 6-8
• High School (9-12)
• Data Analysis and Probability