The distribution(s) of a set of future responses from the multiple regression model with first order auto-correlation, conditional on the realized sample data, has been derived by using the inherent relation of the model. Based on the multivariate normality assumption of the realized but unobserved errors, the maximum likelihood estimate for the coefficient of auto-correlation, has been obtained from the marginal likelihood function. This estimate has been used for the estimation of the combined (realized and future) error vector's covariance matrix, which appears in the prediction density of the future responses. The prediction distribution has been found to be a multivariate Student-t distribution whose degrees of freedom depends on the size of the observed sample and the dimensionality of the regression parameter vector. The results have been generalized for the multilinear model. Some applications of prediction distribution for different linear models have been cited.