The accompanying data file contains annual population data (in millions) for Japan from 1960 to 2017. For cross-validation, let the training and the validation sets comprise the periods from 1960 to 2005 and 2006 to 2017, respectively. 

a. Use the training set to estimate the linear, the quadratic, and the cubic trend models and compute the resulting MSE, MAD, and MAPE for the validation set. 

b. Determine the preferred model and reestimate it with the entire data set to forecast the population in Japan for 2018.