CASE STUDY 2 (Least Squares Approximation-Discrete / other models) Annual Financial Highlight: SIME DARBY BERHAD (4197) 50000 46,955 45000 43,729 43,963 43,084 44,483 40000 35000 7.9 36,156 33,828 30000 5.5 5.7 25000 20000 15000 2.2 10000 5000 3,701 2013-06-30 2,402 1,919 0 820.0 2014-06-30 2018-06-30 2020-06-30 Profit Margin (%) Profit After Tax (RM mil) Revenue (RM mil) Figure 2 (https://www.malaysiastock.biz/Corporate-Infomation.aspx?securityCode=4197) a) Above is the graph showing the annual financial performance of a business company known as SIME DARBY BERHAD. By using the following Profit Margin data (% - blue line) in Figure 2, i) Construct the Newton's Finite divided-difference table up to the fourth (4th) order. (Note: The use EXCEL software are allowed) (5 marks) 44,447 7.5 3,353 2,313 2015-06-30 5.5 2,357 2017-06-30 2016-06-30 948.0 2019-06-30 36,934 3.2 1,425 10,673 236.0 2022-06-30 (10) 2021-06-30 b) Find Lagrange Interpolating polynomial for the given values in Table 1 in (i). Hence use the polynomial to approximate y=f(x) on i) 13 January, 2022 ii) 03 March, 2022 (12 marks) c) Make conclusions on the accuracy of the approximations, in comparison to the exact data given in the website. (3 marks) CASE STUDY 2 (Least Squares Approximation-Discrete / other models) Annual Financial Highlight: SIME DARBY BERHAD (4197) 50000 46,955 45000 43,729 43,963 43,084 44,483 40000 35000 7.9 36,156 33,828 30000 5.5 5.7 25000 20000 15000 2.2 10000 5000 3,701 2013-06-30 2,402 1,919 0 820.0 2014-06-30 2018-06-30 2020-06-30 Profit Margin (%) Profit After Tax (RM mil) Revenue (RM mil) Figure 2 (https://www.malaysiastock.biz/Corporate-Infomation.aspx?securityCode=4197) a) Above is the graph showing the annual financial performance of a business company known as SIME DARBY BERHAD. By using the following Profit Margin data (% - blue line) in Figure 2, i) Construct the Newton's Finite divided-difference table up to the fourth (4th) order. (Note: The use EXCEL software are allowed) (5 marks) 44,447 7.5 3,353 2,313 2015-06-30 5.5 2,357 2017-06-30 2016-06-30 948.0 2019-06-30 36,934 3.2 1,425 10,673 236.0 2022-06-30 (10) 2021-06-30 b) Find Lagrange Interpolating polynomial for the given values in Table 1 in (i). Hence use the polynomial to approximate y=f(x) on i) 13 January, 2022 ii) 03 March, 2022 (12 marks) c) Make conclusions on the accuracy of the approximations, in comparison to the exact data given in the website