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An appliance repair shop owner has fitted the quadratic trend equation ŷ = 90 + 0.9x + 3x² to a time series of annual repair orders, with y= the number of repair orders and x= 1 for 2000. Forecast the number of repair orders for 2008; for 2010

  • statistics -

    This is really a problem of evaluation of functions.

    As indicated, for year
    2000, x=1, so for
    2008, x=2008-1999=9, and for
    2010, x=2010-1999=11

    Let
    y = f(x) = 90+0.9x+3x²
    for 2000, f(1) = 90 + 0.9*(1) + 3*1² = 93.9
    for 2008, f(9) = 90 + 0.9*(9) + 3*9² = 341.1
    for 2010, f(11)= 90 + 0.9*(11) + 3*11² = 462.9

    Note that in general, the number of repairs is an integer (whole number), so the estimate should be rounded to the nearest integer.

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