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  1. #1
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    Help Again




    If forgot, I had one more. I'm stuck on this equation too:

    A quadratic regression model is fit to a set of sample data consisting of 6 pairs of data. Given that the sum of squares of residuals is 18.17 and that the y-values are 11, 14, 19, 22, 26, 27, find

    R^2 = 1 - {The sum of (y - the predicted value of y)^2}
    divided by:{The sum of y - the mean of y)^2}

    So I tried to put the numbers in the equation:
    R^2 = 1 - 18.17^2 divided by:
    119 - 19.833

    fyi: 18.17 = (the sum of squares of residuals); (119= the sum of y) and
    (19.833 = the mean of y)

    What am I doing wrong?

  2. #2
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    In your equation:

    R^2 = 1 - {The sum of (y - the predicted value of y)^2}
    divided by:{The sum of y - the mean of y)^2}

    Although I'm not completely sure, I think it should actually be:

    1 - [ {sum of (y - the predicted value of y)^2} / {sum of y - the mean of y)^2} ]

    In other words 1 - [ the fraction of everything else ]

    = 1 - [ ( 18.17^2 / (119 - 19.833)^2 ) ]

    = 1 - .0336 = .9664

    With an r^2 value this high, the regression line should fit the points very closely - is that the case?


  3. #3
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    John,

    My question is this:

    Did I put the numbers in correctly? (It's hard to write ot the question as it appears on the paper. So I have to substitute since there is no "mean" sign available.)

    Was 18.17 in the correct place? I mean, according to the question is the sum of (y - the predicted value of y)^2 - is that where sum of squares of residuals is 18.17 is supposed to be?

    I hope I'm not confusing you. Please help.

    I tried to put the answer .966 in the homework model and it showed incorrect.

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    As far as I can tell, everything appears OK. Yes, 18.17 is the sum of squared residuals.

  5. #5
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    I think I found the error-

    this formula:

    1 - [ {sum of (y - the predicted value of y)^2} / {sum of y - the mean of y)^2} ]

    should actually be:

    1 - [ {sum of (y - the predicted value of y)^2} / {sum of (y - the mean of y)^2} ]

    which would give you:

    1 - [ 18.17 / 206.833 ]

    = 1 - .0878 = .9122

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    Thanks


    Thanks John. I must have did my numbers incorrectly. Thanks again.

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