A battery manufacturer has been a leading producer for over half a century. Several decades ago, the company used the monthly sales (in millions of batteries) of one battery model to develop the following prediction model: yˆ = 15.0 + 0.5t − 0.000525t 2 (1) where t is the number of months since the recording began and yˆ is the predicted 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.
(a) Plot the model of the monthly sales alongside the actual sales. Does it appear that the model is correct? (Hint: create a column in the Excel file to compute yˆ alongside the given ‘months’ and ‘sales(millions)’ columns, then create a graph)
(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 first 15 years, section 2 for years 16 to 20, and section 3 for years 21 to 25. Compute the MAPE for each section. What can you say about the accuracy of the model.
(d) After some analysis, a new model is proposed: yˆ = 14.5 + 0.5t − 0.000585t 2 (2) where t is the number of months since recording began and yˆ is the predicted volume of sales. Using MAPE, determine if the new proposed model is a better fit than the original model.
(e) Use the new model (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. 1). What is the difference in prediction? Do you believe the recalculation of the model was necessary?