5. [15%] A battery manufacturer has been a leading producer for over half a century. Several decades ago, the company used the monthly sales (in mil- lions of batteries) of one battery model to develop the following prediction model: 3} = 15.0 + 0.51% 0.000525t2 (l) where t is the number of months since the recording began and? is the pre- dicted volume of monthly sales. During the first years, the predictions were close to the actual monthly sales, so the model was assumed to be correct. It has been 25 years now since the beginning of the prediction model and its predictions have come into question. The monthly sales data is found in le BA3653FinalExamBattery.xlsx. (3) Plot the model of the monthly sales alongside the actual sales. Does it appear that the model is correct? (b) Calculate the cumulative sum of forecast errors (CFE). Do you believe there is a bias in the prediction? (c) Divide the data into three sections: section 1 for the rst 15 years, section 2 for years 16 to 20, and section 3 for years 21 to 25. Compute CFE and MAPE for each section. What can you say about the accuracy of the model. (d) After some analysis, a new model is proposed: 3'} = 14.5 + 0.515 0000585152 (2) where t is the number of months since recording began and?) is the predicted volume of sales. Calculate the CFE comparing the data and the new model. Do you believe a bias is present? (e) Using MAPE, determine if the new proposed model is a better fit than the original model. (f) Use the new mode] (Eq. 2) to predict sales for the twelfth month of year 30. Recalculate the sales prediction for the same month using the original model (Eq. I). What is the difference in prediction? Do you believe the recalculation of the model was necessary? (g) From experience, the company knows that monthly sales have a range of variation of :l: 6 million batteries. Using this information, estimate the approximate time when the model should have been revised