The classical regression model leads to effective statistical analysis of precise, numeric, and statistical data. Over the past two decades, in order to cope with imprecise data coming from fuzzy environments where human(expert) subjective estimates are used, various fuzzy regression models have been introduced. Most of the existing studies on fuzzy regression analysis have focused on data consisting of numeric values, interval-like numbers, or fuzzy numbers without randomness into considerasion. In practical situations, however, there exists a genuine need to cope with data that involves the factors of both fuzziness and probability. In order to address regression problems in the presence of such hybrid uncertain data, fuzzy-random variables are introduced in this thesis to serves as an integral component of regression models. A new class of fuzzy regression models that is based on fuzzy-random data is built, and is called the confidence-interval-based fuzzy- random regression model(CI_FRRM). First, a general fuzzy regression model for fuzzy- random data is introduced. Then based on credibility measure, the expected value of a fuzzy variable is presented, by using expectation and variances of fuzzy-random variables, sigma-confidence interval are constructed for fuzzy-random input-output data. The CI-FRRM is established based on the sigma-confidence intervals. The proposed regression model gives rise to a nonlinear programming problem that consists of fuzzy numbers or interval numbers. Since sign changes in the fuzzy coefficients modify the entire programming structure of the solution process, the inherent dynamic nonlinearity of this optimization makes it difficult to exploit the techniques of linear programming or classical nonlinear programming. To remove this difficulty and derive the optimal model, we consider two approaches: a vertic method to describe the model and a realistic model. Finally, explanatory examples is provided to illustrate and investigate the proposed fuzzy-random regression model.