Question 3. (a) (i) Discuss the main advantage of using a moving-average to represent time-series data. [2 marks] (ii) In a particular country, the number new infections of COVID-19 is illustrated by a 7-day moving average. In today's COVID-19 report for the number of new infections, the 7-day moving average has dropped, but the actual number of infections has increased. What can you say about the pattern of new COVID-19 infections? [3 marks] (b) The sales for soca CDs at a music store follows a seasonal pattern with a trend. The following deseasonalised data is to be used: Year Quarter 1 Quarter 2 Quarter 3 Quarter 4 2010 24 26 26 28 2011 29 28 30 33 The seasonality indices (calculated over many years' data) are given to be: Quarter 1 1.5 Quarter 2 0.9 Quarter 3 0.7 Quarter 4 Using the Decomposition Method, predict the sales figures for the four quarters of 2012. [10 marks] (c) Companies in a modern telecommunications industry attempt to influence sales by advertising on social media and on billboards around the country. To boost their marketing campaigns, these companies sometimes use an A-list celebrity, or a B-list celebrity as the spokesperson for the company. A regression relationship for sales in '000,000s) is created using social media advertising costs (XI in "000s of S), number of billboards (X2), and the presence of a celebrity (X3 and X4). The following regression results were obtained: Variable Coefficient Intercept 0.275 XI 0.45 X2 0.512 page 5 0.75 X3 - 1 if a Tier I celebrity is used - otherwise 0.63 X4-1 if a Tier-2 celebrity is used - otherwise (i) Predict the sales value when $200,000 is spent on social media advertising, 6 billboards are used, and an A-list celebrity is used in the marketing campaign. [3 marks] (ii) Determine the maximum that the company should pay for a B-list celebrity [2 marks]