How much can one point move the line of best fit?

Open the Interactive Regression Line (Geogebra). Move the blue point “P”, and see what effect it has on the red line.

1 Move P so that it is centered amongst the other points. Now move it all the way to top and bottom of the screen.

2 Move P so that it is far to the left or right of the other points. Now move it all the way to top and bottom of the screen. How - if at all - does the x-position of P impact on the line of best fit?

3 Could the regression line ever be above or below all the points (including the blue one you’re dragging)? Why or why not?

4 Would it be possible to have a line with more points on one side than the other? Why or why not?

5 What is the highest r-value you can get? Where did you place P? (, )

6 What function describes the regression line with this value of P? y = x +

7 What is the lowest r-value you can get? Where did you place P? (, )

8 What function describes the regression line with this value of P? y = x +

Predictions from Scatter Plots

weeks-v-age scatter plot with some points in the lower left and some in the upper right

weeks-v-pounds scatter plot with a tight cluster in the lower left and some points toward the right and top right corner

9 Draw the line of best fit for age-v-weeks (on the left). Is this a strong correlation that will allow us to make a good prediction of an animal’s adoption time just by knowing how old it is?

10 Draw the line of best fit for pounds-v-weeks (on the right). Is this a strong correlation that will allow us to make a good prediction of an animal’s adoption time just by knowing how heavy it is?

11 Do either or both of the relationships appear to be linear?

These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). CCbadge Bootstrap by the Bootstrap Community is licensed under a Creative Commons 4.0 Unported License. This license does not grant permission to run training or professional development. Offering training or professional development with materials substantially derived from Bootstrap must be approved in writing by a Bootstrap Director. Permissions beyond the scope of this license, such as to run training, may be available by contacting contact@BootstrapWorld.org.