The following questions relate to the residuals analysis reported in Tables 11.4 and 11.5. (a) Compute s 2 ( i ) + s 2 (e i ) for several choices of i. How do you explain the fact that you obtain very...

(a) Compute s₂(
_i) + s₂(e_i) for several choices of i. How do you explain the fact that you obtain very nearly the same number each time?

(b) Find the largest and smallest s(
_i) and the largest and smallest vii. Explain why they derive from the same observations in each case.

(c) A COVRATIO equal to 1.0 implies that the ith point has no real impact on the overall precision of the estimates. A COVRATIO less than 1.0 indicates that the presence of the ith observation has decreased the precision of the estimates (e.g., Observation 12). How do you explain the presence of an additional observation causing less precision?

(d) Cook’s D provides a measure of the shift in β. The DFBETAS measure shifts in the individual β_j. How do you explain the fact that Observation 29, which has the largest value of Cook’s D, has no DFBETASj that exceed the cutoff point, whereas Observation 34, which has the next to the largest value of Cook’s D, shows major shifts in all but one of the regression coefficients? Conversely, explain why Observation 10 has a small Cook’s D but shows major shifts in the intercept and the regression coefficients for pH and Z_n.