In regression analysis, an investigator may be misled by some unusual observations which have strong influence in estimating the regression coefficients. In such case, we need to determine whether we should put more emphasis on those influential observations or ignore them in subsequent analysis. To do so, we obtain an influence function to see how our estimates are influenced by a single observation. Cook(1977, 1979) introduced an influence function for each individual observation, which measures the difference in standard deviation units between the estimates with and without the observation. In this research, we derive influence function, using Cook's distance, for estimating the regression coefficients under univariate multiple regression model when the stochastic or non-stochastic prior information is uncertain. We also extend the influence function result from univariate model to multivariate model.