The U.S. Air Force uses regression models for cost estimating, an application that almost always involves outliers. Simpson and Montgomery [1998a] present 19 observations on first-unit satellite cost data \((y)\) and the weight of the electronics suite \((x)\). The data are shown in the following table.

a. Draw a scatter diagram of the data. Discuss what types of outliers may be present.
b. Fit a straight line to these data with OLS. Does this fit seem satisfactory?
c. Fit a straight line to these data with an \(M\)-estimator of your choice. Is the fit satisfactory? Discuss why the \(M\)-estimator is a poor choice for this problem.
d. Discuss the types of estimators that you think might be appropriate for this data set.

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Observation Cost ($K) Weight (Ib) 1 2449 90.6 13 14 15 18 19 23456789OUDERATED 2248 87.8 3545 38.6 794 28.6 1619 28.9 2079 23.3 918 21.1 1231 17.5 3641 27.6 10 4314 39.2 11 2628 34.9 12 3989 46.6 2308 80.9 376 14.6 5428 48.1 16 2786 38.1 17 2497 73.2 5551 40.8 5208 44.6