In this some new estimation methods and testing procedures for the linear regression models with heteroscedastic disturbances. A Minimum Norm Quadratic Unbiased (MINQU) estimation method has been developed for estimating the unknown heteroscedastic error variances by using the weighted studentized residuals. A multiplicative heteroscedastic linear regression model has been specified and a method of estimating the parameters of linear regression model along with the in the heteroscedastic error variance has been given by using the predicted residuals. Three types of modified estimators have been proposed for the parameter of multiplicative heteroscedastic error variance by using internally studentized residuals.an adaptive method of estimation has been suggested to estimate the heteroscedastic error variances based on Bartlett’s test by using the internally studentized residuals. Besides these new estimation methods, the testing procedures for testing the equality between the regression coefficients in two/sets of linear regression models under heteroscedasticity have been suggested by using the studentized residuals.