SUMMARY Y is a linear regression on a variable X; X is fixed and all its sample values are observed. Y, on the other hand, has some sample values missing. This work outlines a maximum likelihood (ml) procedure that tries to adjust for bias due to non-random missingness; here non-randomness is specified by a logistic distribution. The ml procedure is implemented via two iterative technologies, namely the EM algorithm (of Dempster, Laird & Rubin, 1977) and the Newton-Raphson method. Data from a dialysis study are used to illustrate our estimation procedure, and results show that the ml procedure is quite effective in adjusting for bias.