Twin parametric insensitive support vector regression(TPISVR) is a novel machine learning method proposed. Compared to other regression methods, TPISVR has unique advantages in dealing with heteroscedastic noise. Standard TPISVR can be attributed to solve a pair of quadratic programming problem(QPP) with inequality constraints in the dual space. However, this method is subject to the constraints of time and memory when number of samples are large. This paper introduces the least squares ideas, and proposes the least squares twin parametric insensitive support vector regression(LSTPISVR) which transforms the two QPPs of TPISVR into linear equations and solves them directly on the original space. Further, a chaotic cuckoo optimization algorithm is introduced for parameter selection of LSTPISVR. Experiments on artificial datasets and UCI datasets show that LSTPISVR not only has fast learning speed, but also shows good generalization performance.