This paper is a technical report of analyses carried out to determine the effects of parents' involvement in a prekindergarten program on their children's cognitive development. The research was part of a longitudinal study of the New York State Experimental Prekindergarten Program. A multiple linear regression approach was used to test hypotheses of interest. The analysis was designed to determine whether the number of hours of parent involvement was related to cognitive development, whether the relationships were curvilinear, whether there were interactions between variables, and whether the relationships could be explained by other variables, including pretest performance, age, mother's education, and family income. The analysis showed that parent involvement had a favorable effect on general reasoning, school-related knowledge and skills, and knowledge of verbal concepts. The effects were found regardless of the child's age, mother's education, or family income. For general reasoning and school related knowledge and skills, the effects were also found, regardless of the child's score on the same test at the beginning of prekindergarten. For knowledge of verbal concepts, however, the effect of parent involvement tended to be greater for children who were initially lowest in knowledge of verbal concepts. (Author/SS)