This research article explores some misspecification tests for stochastic linear regression model viz. Durbin-Watson test, Ramsey's regression specification error test, Lagrange's multiplier test, and UTTS' rainbow test. Any type of error occurred in the set of underlying assumptions of a stochastic linear regression model and the associated inferences lead to 'specification errors'. These errors will present particularly in specifying the error vector ϵ and the data matrix X. Generally specification errors are caused by the inclusion of irrelevant independent variables or exclusion of relevant independent variables in the stochastic linear regression model. Ivan Krivy et.al, in 2000 in their research article depicted two stochastic algorithms which are useful in estimating the parameters of nonlinear regression models. Russell Davidson et al. in 1984 (see [2]), in their paper, developed a simple computational procedure for performing a wide variety of model specification tests. In1993, LudgerRuschendorf et.al in their research article constructed as nonlinear regression representations of general stochastic processes so that they got a particular special regression representations on Markov chains and of certain m- dependent sequences. © 2019 Author(s).