There are often some prior requirements about empirical risk in regression problems. To meet these requirements, this paper firstly proposes two novel support vector regression machine models in which part of empirical risks are given. One is a support vector regression machine in which partial empirical risks are given (PSVR), and the other is a model in which unilateral partial empirical risks are given (UPSVR). For the samples with given empirical risk levels, PSVR meets the requirements by some inequality constraints about empirical risk levels, while for the other samples without empirical risk requirement, PSVR uses the same strategy as the tradition support vector regression (SVR) to meet the requirement of empirical risk. UPSVR is similar to PSVR, except that the inequality constrains of empirical risks are unilateral. Secondly, the dual problems and the solving methods of PSVR and UPSVR are given. Finally, the effectiveness and superiority of PSVR and UPSVR are verified by the experiments on four artificial datasets. Both PSVR and UPSVR achieve better regression performance than the traditional models respectively. At the same time, PSVR is less sensitive to the trade-off coefficient C between empirical risk and confident risk compared with SVR. Thus, PSVR can select parameter C faster and more conveniently. PSVR and UPSVR are the extensions of the traditional models. When the set of samples with given empirical risks is empty, they degenerate into the traditional models. PSVR and UPSVR are suitable for the scene with prior requirements of empirical risk.