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The usual approach to handling missing data in a regression is to assume that the points are missing at random (MAR) and use either a fill-in method to replace the missing points or a method using maximally available pairs in the sample covariance matrix. We derive limits for the values of the least squares estimates of the coefficients (and their associated t statistics) when there are missing observations in one carrier. These limits are derived subject to a constraint on the relationship of the missing data to the present data. Calculating these limits while varying this constrained value results in a series of diagnostic plots that can be used to study the potential effect of the missing points on the regression (without assuming that the points are MAR). Simulations are performed to illustrate the use of the plots, and two real data sets are analyzed. The more general case of missing data in more than one carrier is also discussed.
Simon et al. (1986) studied this question.