In research and statistics projects, if we know the form of the regression, parametric inferences often perform better than semiparametric inferences and nonparametric inferences. In this literature, we give an algorithm of parametric maximum likelihood estimator(MLE) under the uniform distribution with linear regression data. We also give some examples which the Newton Raphson(NR) method may not work but the MLE can be computed by our algorithm. Moreover, we propose diagnostic plotting method and test to a data set.