Describe how the least-squares regression line, standard deviation of the residuals, and r2 are influenced by outliers.
Find the slope and y intercept of the least-squares regression line from the means and standard deviations of x and y and their correlation.
Activity: How do outliers affect the LSRL?
For this activity, students used this Correlation and Regression applet. Each pair of students created their own scatterplot with 10 points and a correlation value, r, around 0.4. The first big idea for them to discover is the LSRL will always pass through the point (mean of x, mean of y).
Caution: Many of our students thought that the horizontal and vertical lines in the applet were the x-axis and y-axis. They are not! They are the values which represent the mean of all the x values and the mean of all the y values. So the crosshair of the two lines is the point (mean of x, mean of y).
Then they added several different types of outliers to see what happens to the slope and y-intercept of the LSRL and whether the correlation will increase or decrease. Pro tip: To remove a point on the applet, simply click on it a second time and it will disappear. This is helpful for students when moving from analyzing one type of outlier to another type of outlier.
Teaching Tip: Descriptor
In the debrief of the activity, we started thinking about the LSRL as being a teeter-totter, where the point (mean of x, mean of y) is the fulcrum or hinge for the teeter-totter. We discovered that outliers in the horizontal direction (or x direction) tended to “tilt” the line towards themselves, while outliers in the vertical directions (or ydirection) tended to “lift” the line up or down. This thinking made it easier to understand what was happening to the slope, y-intercept, and correlation value.
Notice that we spent very little time on the last learning target. This was intentional. We don’t feel as if it provided much insight into better understanding AND the formulas are provided on the AP Exam. So we did mention it in the Big Ideas and had students try one problem in the Check Your Understanding.