Question: a. Use the Minitab macro LMSONEX to compute the LMS estimator, and use LTSONEX to compute the exact LTS(.25) estimator for the following data set.
b. Determine which points were trimmed for the LTS(.25) estimator by looking at the ordered squared residuals.
c. Now construct a scatter plot. Does the set of deleted points seem reasonable relative to your scatter plot? What does your scatter plot suggest should be done first: plot the data or obtain point estimates for an assumed model?
d. Use the Minitab macro EXACTLMS to obtain the exact LMS solution. Notice that there is a dual solution. Can this be determined from inspection of the scatter plot? Notice that many of the Cheby-shev fits do not exist because many point triplets constitute exact fits. Could one of these exact fits have produced the exact LMS solution? Explain. Could one of the two triplets for which the regression equation does not exist have produced the exact LMS solution?
e. Assume that the three points with the largest x-coordinates are errors and thus should be deleted. What would be the OLS equation computed from the remaining points? Is this equation apparent from either the scatter plot or the list of the data?
f. What must be the LMS equation computed from these 11 points? What property determines the equation in this instance? Remembering that the LMS estimator is designed to fit the majority of the data, and thus protect against outliers, do either of the exact LMS solutions for the 14 data points seem desirable relative to the configuration of good data points?