Selection bias: Suppose the normal linear model ????i = ????0 + ????1xi holds with

????1 > 0, but the responses are truncated and we observe yi only when yi > L

(or perhaps only when yi < L) for some threshold L.

a. Describe a practical scenario for which this could happen. How would you expect the truncation to affect ????̂

1 and s? Illustrate by sketching a graph.

(You could check this with data, such as by fitting the model in Section 3.4.1 only to house sales having yi > 150.)

b. Construct a likelihood function with the conditional distribution of y, to enable consistent estimation of ????. (See Amemiya (1984) for a survey of modeling with truncated or censored data. In R, see the truncreg package.)