Question: Consider the data in Table, for which the fitted regression equation should ideally have a slope of zero. For which of the following estimators would we expect the slope to be approximately zero when applied to this data set:
(a) LMS or
(b) LTS(.25), or both?
How many observations will be effectively trimmed if LTS(.25) is used with the definition of it given? When LMS is used with the PROGRESS approach and all exact fits are used, 22 points receive a weight of zero when reweighted least squares is used: 2, 4, 5, 7, 12-14, 19, 22, 23, 25-27, 31, 32, 40, 44, 64, 71, 77, 80, and 83. When LTS(.25) is used, 24 points are deleted, and they are: 2, 4, 5, 6, 12-14, 35-51. When the sequential LTS approach is used with a stopping rule of 3, the points that are deleted are 2, 4, 5, 6, 12, 13, and 46-51. [The Hawkins approach with 20 random starts was used for the sequential LTS approach, and 100 random starts were used for LTS(.25).] Compute the least-squares regression line using each set of retained points and look at, in particular, the p-value for the slope for each equation. Do all three approaches suggest that the true slope is zero?
