The accompanying data file con$$tains annual population data $($in millions$)$ for Japan from $1960$ to $2019.$ For cross$-$validation, let the training and the validation sets comprise the periods from $1960$ to $2005$ and $2006$ to $2019,$ respectively.

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a$.$ Use the training set to implement the Holt exponential smoothing method with user$-$supplied $(\backslash$alpha $=0\mathrm{.}20$ and $\backslash$beta $=0\mathrm{.}15),$ as well as the computer$-$generated, smoothing parameters and compute the resulting performance measures for the validation set.

Note: Do not round intermediate calculations. Round final answers to $2$ decimal places.

b$-1.$ Determine the preferred smoothing parameters for making the forecast?

b$-2.$ Reestimate the preferred model with the entire data set to forecast the population in Japan for $2020($in millions$).$

Note: Do not round intermediate calculations. Round final answers to $2$ decimal places.