Daily high temperatures in St. Louis for the last week were as​ follows: 95​, 92​, 93​, 92​, 95​, 90​, 90 ​(yesterday). ​a) The high tempera

Question

Daily high temperatures in St. Louis for the last week were as​ follows: 95​, 92​, 93​, 92​, 95​, 90​, 90 ​(yesterday). ​a) The high temperature for today using a​ 3-day moving average ​= 91.7 degrees ​(round your response to one decimal​ place). ​b) The high temperature for today using a​ 2-day moving average ​= 90 degrees ​(round your response to one decimal​ place). ​c) The mean absolute deviation based on a​ 2-day moving average​ = 1.9 degrees ​(round your response to one decimal​ place). ​d) The mean squared error for the​ 2-day moving average​ = nothing degrees squared ​(round your response to one decimal​ place).

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Kinsley 3 weeks 2022-01-06T21:43:43+00:00 1 Answer 0 views 0

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    2022-01-06T21:45:12+00:00

    Answer:

    a) T = 91.7 degrees

    b) T = 90 degrees

    c) MAD = 1.9

    d) MSE = 5.05

    Step-by-step explanation:

    Given:

    – Daily high temperatures in St. Louis for the last week were as​ follows:

                                       95​, 92​, 93​, 92​, 95​, 90​, 90

    Find:

    a) Forecast the high temperature today, using a 3-day moving average.

    b) Forecast the high temperature today, using a 2-day moving average.

    c) Calculate the mean absolute deviation based on a 2-day moving average, covering all days in which you can have a forecast and an actual temperature.

    d) The mean squared error for the​ 2-day moving average​

    Solution:

    a)

    – The set of 3 day moving average is as follows:

    4.   (95 + 92 + 93) ÷ 3 = 93.33⁰C

    5.  (92 + 93 + 92) ÷ 3 = 92.33⁰C

    6.  (93 + 92 + 95) ÷ 3 = 93.33⁰C

    7.  (92 + 95 + 90) ÷ 3 = 92.33⁰C

    8.  (95 + 90 + 90) ÷ 3 = 91.667⁰C

    – Now use these points on excel sheet to forecast the temperature for today. The line of best fit is given:

    T = 91.7 degrees

    b)

    – The set of 2 day moving average is as follows:

    3.   (95 + 92) ÷ 2 = 93.5⁰C

    4.  (95 + 93) ÷ 2 = 92.5⁰C

    5.  (93 + 92) ÷ 2 = 92.5⁰C

    6.  (92 + 95) ÷ 2 = 93.5⁰C

    7.  (95 + 90) ÷ 2 = 92.5⁰C

    8. (90 + 90) ÷ 2 = 90⁰C

    – Now use these points on excel sheet to forecast the temperature for today. The line of best fit is given:

    T = 90 degrees

    c)

                                 Error             Error^2

    3.   93.5⁰C            0.5                  0.25

    4.   92.5⁰C            0.5                  0.25

    5.   92.5⁰C            2.5                  6.25

    6.   93.5⁰C            3.5                  12.25

    7.   92.5⁰C            2.5                  6.25

    8.   90⁰C

    – The mean absolute deviation as follows:

                                  MAD = Sum of all errors  / 5

                                  MAD = (0.5+0.5+2.5+3.5+2.5)  / 5

                                  MAD = 1.9

    d)

    – The mean squared error deviation as follows:

                                  MSE = Sum of all error^2  / 5

                                  MSE = (0.25+0.25+6.25+12.25+6.25)  / 5

                                  MSE = 5.05

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