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QUALITY DATA ANALYSIS 18/06/2021 General recommendations: • write the solutions in CLEAR and READABLE way on paper and show (qualitatively) all the relevant plots; • avoid (if not required) theoretical introductions or explanations covered during the course; • always state the assumptions and report all relevant steps/discussion/formulas/expression to present and motivate your solution; • when using hypothesis tests provide the numerical value of the test statistic and the test conclusion in terms of p-value. • For exams in presence: to access the software on the provided laptops, go on browser → Favourites → Managed favourites → Virtual Desktop and enter your Polimi credentials. • Exam duration: 2h 10min Exercise 1 (15 points) The energy consumption of a thermal treatment facility is known to follow a time series model 𝑥𝑡 = 𝛽0 + 𝛽1𝑥𝑡−1 + 𝜀, with 𝜀~𝑁(0, 𝜎𝜀 = 0.65). Based on historical process data, the unknown coefficients estimates are available 𝛽0̂ = 𝑏0 and 𝛽1̂ = 𝑏1 and one can assume that 𝐸(𝑏0) = 9.5, 𝑉(𝑏0) = 6.5, 𝐸(𝑏1) = 0.64, 𝑉(𝑏1) = 0.0196. Every month, 30 consecutive measurements (in KWh) are collected. The data collected in June and July 2020 are reported in Table 11. Table 1 Month Order Measured value Order Measured value June 1 26,01 16 26,47 2 26,72 17 26,12 3 25,24 18 26,64 4 25,63 19 27,02 5 25,66 20 27,32 6 24,87 21 27,19 7 24,68 22 26,15 8 24,92 23 26,28 9 26,72 24 26,84 10 27,76 25 26,71 11 26,54 26 26,89 12 27,75 27 26,87 13 27,56 28 26,35 14 27,02 29 26,23 15 26,97 30 25,59 Month Order Measured value Order Measured value July 1 26,5 16 26 2 23,74 17 24,64 3 25,83 18 26,64 4 25,47 19 25,14 5 25,72 20 25,68 6 25,6 21 24,6 7 25,38 22 26,09 8 25,67 23 25,03 9 25,16 24 25,78 10 26,13 25 25,25 11 24,44 26 25,93 12 26,36 27 24,84 13 24,56 28 26,01 14 25,9 29…