Quarterly profits, Y1, (in million ) made by a manufacturing firm for the past five years 3]. [40%] are given in the following Table. Table 3: Quarterly protit in minon puunuo You must select your own values of Y1 and Y20 randomly from below. Possible values for Y1 are [35,35.5,36,36.5,37, 37.5,38,38.5,39,39.5,40] Possible values for Y20 are [55,55.5,56,56.5,57,57.5,58,58.5,59,59.5,60] To analyse this data, a time series model containing trend and seasonality is proposed. a) Describe fully an appropriate dummy variable regression model to analyse the time series. Specify the assumptions involved in fitting the model and discuss how they can be checked graphically. [10 marks] b) Analyse the data fully by fitting your model (using Minitab) and interpret the results. Obtain the profit forecast for each quarter of 2023 and their 95% prediction intervals. Interpret your prediction intervals. Attach your Minitab output (at most 2 pages!) with your coursework. [10 marks].