This paper employs daily trading data during 1992 to 1994, of 8 industry indexes and of 36 sample stocks traded on Taiwan Stock Exchange, to investigate if the market model (estimated by OLS method), which is popularly used in the financial area, follows or violates the basic assumptions of normal linear regression model. This paper also provides a estimation procedure for market model under such conditions that basic assumptions are violated. The results shows that among the three basic assumptions (normality, homoskedasticity and nnonautocorrelation of the stochastic disturbance), most of the empirical models violate the basic assumptions of normality and homoskedasticity, especially the assumption of homoskedasticity against autoregressive conditional heteroskedasticity. It should be noted that under heteroskedasticity, the least squares estimates are not efficient and the estimates of the variances are also biased, thus invalidating the tests of significance. Our findings provide strong implications to CAPM related research, such as event studies, market anomalies and market efficiency. Besides it seems that capital sizes are correlated to the violation of heteroskedasticity (under Breusch-Pagan tests), and it seems that the larger the capital size, the easier to violates the assumption of homoskedasticity. Finally, by taking the Cement Industry Index as example, which simultaneously violate the basic assumptions of normality, homoskedasticity and nonautocorrelation, this paper demonstrates a procedure for correctly estimating the regression coefficients. The suggesting estimation procedure should not be neglected by a rigorous academic research.