This study addresses the challenge of fitting a simple linear regression model to data with missing or censored values by presenting a novel approach based on the Expectation–Maximization algorithm. The proposed approach is developed to estimate the parameters of models under various incomplete data scenarios, including missing, left censored, right censored, and interval censored observations in bivariate normal data. Extensive simulation studies evaluate the performance of the proposed approach across varying sample sizes, incomplete proportions, and correlations between variables. The study compares the proposed approach with the existing models, which ignores incomplete observations in model fitting. Evaluation metrics including
bias, variance, Root Mean Squared Error, Coverage Probability, and Relative Root Mean Squared Error are used to assess the estimates from both approaches. The proposed method is applied to real datasets to validate its effectiveness against naive estimates. Standard error, confidence interval, and interval width assess the precision and accuracy of parameter estimates for both models, while the Akaike Information Criterion selected the best–fitting model. The results show that the proposed approach provides more accurate and precise parameter estimates compared to the naive approach in both simulation studies and real data applications.
