The regression method for analysing changes in variables over the time and cross-section has become very popular in the present day world. The method is undoubtedly very powerful but it is based on several assumptions and if any of its assumptions do not hold good for a particular sample, its results are unacceptable. Unfortunately, many of the users of this technique are unaware of its limitations or/and of the methods of correcting for them. The paper discusses the testing procedures and the appropriate methods of estimation of models which are subject to multicollinearity, a serious problem of regression analysis. The demand for cotton textiles' function is estimated from the time series data of the Indian economy for illustration purposes.