Q$8($Exponential Smoothing Holts Method$)$For the following time series:tY$132539420512617722823952104111561275136014751588($a$)$ Plot the time series and superimpose the linear Trend. Calculate the slope of the Trend from t$=1$ to t$=15$ and comment on whether Holts Trend adjustment method is appropriate for forecasting.$[15$ marks$]($b$)$ Use Holts Trend adjustment method to forecast Y for t$=20$ with $=0\mathrm{.}5,=0\mathrm{.}5.$ Start your calculations from t$=2.$ Start your calculations from t$=2.[10$ marks$]($c$)$ Obtain the values of and which minimize the MSE and superimpose the forecasts on the time series plot. $[10$ marks$]($d$)$ Is your view on the suitability of Holts method justified by the forecast plot? Justify your answer. What do the optimal values of and imply?