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    Least Squares Regression Line and MAD

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    For the data below

    Year Automobile Sales Year Automobile Sales
    1990 116 1977 119
    1991 105 1998 34
    1992 29 1999 34
    1993 59 2000 48
    1994 108 2001 53
    1995 94 2002 65
    1996 27 2003 111

    (a) Determine the least squares regression line.
    (b) Determine the predicted value for 2004.
    (c) Determine the MAD.
    (d) Determine the unadjusted forecasting MSE.

    © BrainMass Inc. brainmass.com March 4, 2021, 9:52 pm ad1c9bdddf
    https://brainmass.com/math/interpolation-extrapolation-and-regression/least-squares-regression-line-mad-279255

    Solution Preview

    Please see attachment.

    LEAST SQUARES REGRESSION LINE
    For the data below
    Year Automobile Sales Year Automobile Sales
    1990 116 1997 119
    1991 105 1998 34
    1992 29 1999 34
    1993 59 2000 48
    1994 108 2001 53
    1995 94 2002 65
    1996 27 2003 111

    (a) Determine the least squares regression line.
    Y X
    Year Automobile sales y =average of sales x =average of year (Y-y) (X-x) (Y-y)(X-x) (X-x)2
    1990 116.00 1.00 71.57 7.50 44.43 -6.50 -288.79 42.25
    1991 105.00 2.00 71.57 7.50 33.43 -5.50 -183.86 30.25
    1992 29.00 3.00 71.57 7.50 -42.57 -4.50 191.57 20.25
    1993 59.00 4.00 71.57 7.50 -12.57 -3.50 44.00 12.25
    1994 108.00 5.00 71.57 7.50 36.43 -2.50 -91.07 6.25
    1995 94.00 6.00 71.57 7.50 22.43 -1.50 -33.64 2.25
    1996 27.00 7.00 71.57 7.50 -44.57 -0.50 22.29 0.25
    1997 119.00 8.00 71.57 7.50 47.43 0.50 23.71 0.25
    1998 34.00 9.00 ...

    Solution Summary

    The expert determines the MAD and the unadjusted forecasting MSE.

    $2.19

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