The values of shear strength parameters

c and φ

estimated by two linear regression methods from data of rock or soil triaxial test are different. To reveal the basic cause of differences between the two regression methods

the principle of linear regression based on the least square method is analyzed thoroughly. The results estimated by regressing maximum principal stress with minor principal stress are the best values

while the results obtained by regressing maximum shear stress with average normal stress are not reliable. Modification for least square method of the latter regression method is done to obtain uniform results. Formulas for calculating modified regression coefficients are deduced. It is proved that results by the two methods after modification are the same; and they are applied to calculate the shear strength parameters in triaxial tests of phyllite. The results show that to rock or soil triaxial test

the values of shear strength parameters calculated by the two methods after modification are also the same best and unbiased estimations.