Question: Consider the following data, with the last three points constituting a cluster of bad data points.

X         1       2       5         3       6       2         4        7          8          9         5         3            4         5        6         3.4        3.7      3.5

Y         5       4       6         2       7       3         5        8          9          9         5         5            7         8        7       15.6       16.2     16.1

Compute the values of DFFITS, DFBETAS, and Cook's-D for the 18 data points, and use 2 as the multiplier in the cutoff value for DFFITS. (If MINITAB is used for this, DFFITS and Cook's-D can be obtained directly, and DFBETAS can be obtained as a by-product from the macro RWLS1DFB. See the discussion in the chapter appendix). Then construct a scatter plot of the data, and use 1.5 as the DFFITS multiplier, as suggested by Staudte and Sheather. What does this suggest about the choice for the multiplier, and more generally, what does it suggest about using single-point diagnostics for detecting multiple outliers? Do the outliers have standardized residuals greater than 2? How many standardized residuals in a sample of n = 18 should exceed 2 if the errors have a nor-mal distribution and there are no bad data points? What does this suggest (combined with what was discussed in the chapter) about routinely using standardized residuals to detect bad data points?
Also compute R² with and without the bad data points. Does this suggest that we should first identify bad data points before (hastily) concluding that there is no linear regression relationship.