Exponential Smoothing SESFor the following time series:tY$148247\mathrm{.}5347446\mathrm{.}5547\mathrm{.}5646747\mathrm{.}5847945\mathrm{.}91046\mathrm{.}511471245\mathrm{.}81345\mathrm{.}91446\mathrm{.}71545\mathrm{.}71647\mathrm{.}11745\mathrm{.}91846\mathrm{.}71946\mathrm{.}22045\mathrm{.}52146\mathrm{.}722452345\mathrm{.}32445\mathrm{.}72546($a$)$ Plot the time series and superimpose the linear Trend. Calculate the slope of the Trend from t$=1$ to t$=25$ and comment on whether simple exponential smoothing is appropriate for forecasting.$[15$ marks$]($b$)$ Use simple exponential smoothing to forecast Y for t$=26$ with $=0\mathrm{.}5.$ Start your calculations from t$=2.[10$ marks$]($c$)$ Obtain the value of which minimizes the MSE and superimpose the forecasts on the time series plot. Is your view on the suitability of simple exponential smoothing justified by the forecast plot? Justify your answer.$[15$ marks$]$