To predict the time-to-failure (TTF) of an engine, we monitored a sample of 100 engine instances using vibration sensors until they failed. The TTF values and their corresponding degradation signals are given in "X.txt" and "Y.txt", respectively. a) Use smoothing splines and functional PCA for dimension reduction and feature extraction. b) Develop prediction models to predict the TTF based on the extracted features. c) Evaluate and compare the performance of the estimated prediction models. Which model do you recommend?