In this paper, we report our recent work on applications of the combined MLLR and MCE approach to estimating the time-varying polynomial Gaussian mean functions in the trended HMM. We call this integrated approach as the minimum classification error linear regression (MCELR), which has been described in this study. The transformation matrices associated with each polynomial coefficients are calculated to minimize the recognition error of the adaptation data and is developed using the gradient descent algorithm. A speech recognizer based on these results is implemented in speaker adaptation experiments using TI46 corpora. Results show that the trended HMM always outperforms the standard HMM and that adaptation of linear regression coefficients is always better when fewer than three adaptation tokens are used.