Based on the FTSMCD method (Two stage multiple change points detection) proposed by Jin, et al. (2016), we tackle the problem of constructing change-points confidence interval estimations in multiple linear regression models. The key idea is to obtain the resampled change-point estimations sequence by using randomly weighted bootstrap method. Using the randomly weighted bootstrap method can get the histogram of the change point estimation, and then we use the Gaussian mixture model to estimate the distribution of the change point. If the parameter changes before and after the change point are small, the randomly weighted bootstrap method will generate redundant change point estimates. Therefore, adding one to the peak number of the histogram is used to determine the number of sub-models in the Gaussian mixture model, which can significantly improve the accuracy of the confidence intervals. Compared with MC simulations, randomly weighted bootstrap simulations perform well and the analysis of weekly NYMEX oil price the daily closing price of the Dow Jones Industrial Average data also reveals the effectiveness of the proposed method.