Try finding the Best Line

Click on the graph to change the blue line so that the residuals (the distance from each point to your line) is the least. The lower the residual, the more your linear function explains the pattern of the data. When you you think you have the best line for the data, click on the "Show" button to see the best fit, and compare the magenta line to your blue line. Note how close your linear equation is to the least squares regression line. Press the "Redo" button to try again with a different set of data.

Reflection Questions

  1. Is there always a "least residual" line?
  2. How often is the average x and y pair on the best residual line? (Note lower left corner to see the (x,y) of the mouse loaction to help you judge this)
  3. Have you found a "recipe" or a "rule of thumb" that allows you to consistantly guess a line very close to the magenta line? What is it?
  4. Is there any connection to the r2 and how easy it is find the least residual line?
The source.