With the wide application of machine learning techniques in practice, privacy preservation has gained increasing attention. Protecting user privacy with minimal accuracy loss is a fundamental task in the data analysis and mining community. In this paper, we focus on regression tasks under $ε$-label differential privacy guarantees. Some existing methods for regression with $ε$-label differential privacy, such as the RR-On-Bins mechanism, discretized the output space into finite bins and then applied RR algorithm. To efficiently determine these finite bins, the authors rounded the original responses down to integer values. However, such operations does not align well with real-world scenarios. To overcome these limitations, we model both original and randomized responses as continuous random variables, avoiding discretization entirely. Our novel approach estimates an optimal interval for randomized responses and introduces new algorithms designed for scenarios where a prior is either known or unknown. Additionally, we prove that our algorithm, RPWithPrior, guarantees $ε$-label differential privacy. Numerical results demonstrate that our approach gets better performance compared with the Gaussian, Laplace, Staircase, and RRonBins, Unbiased mechanisms on the Communities and Crime, Criteo Sponsored Search Conversion Log, California Housing datasets.