Final answer:
To identify potentially influential observations, one examines the effect of removing these points on the regression line's slope or the correlation coefficient. Using Rule 1 (4*mean) and Rule 2 (residuals greater than 2s or less than -2s), we can identify outliers that may be influential if their removal significantly alters the regression analysis.
Step-by-step explanation:
To identify potentially influential observations in a data set, two rules are considered. Rule 1 utilizes the mean and four times the standard deviation (4*mean) while Rule 2 uses a horizontal line representing the cutoff value of 1. Observations that are potentially influential are those that significantly change the slope of the regression line if they were to be removed.
We are looking for outliers using the criterion that any point with a residual greater than 2 times the standard deviation (2s) or less than -2s from the line of best fit is an outlier. Applying this to Rule 2, an outlier would have a residual greater than 32.8 or less than -32.8 using the given standard deviation of 16.4. Similarly, any points deviating from the cutoff based on Rule 1 would also indicate potential influence.
If an outlier identified by these rules is removed, and the correlation coefficient (r) or the slope of the regression line changes significantly, it is confirmed as an influential point.