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Statistics: given total sum of squares, find R²

  1. Oct 4, 2014 #1

    939

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    1. The problem statement, all variables and given/known data

    Given:
    Σ(xi - x̄)² = 500
    Σ(yi - ybar)² = 800 (total sum of squares, SST))
    Σ(ŷ - ybar)² = 400 (total sum of estimators, SSE)
    Σ(xi - x̄)²(yi) = 200
    Σ(xi - x̄)²(εi) = 0
    n = 1000
    s² = 4

    Find (or explain why you cannot find):
    β1
    β0
    variance of β


    2. Relevant equations

    Σ(xi - x̄)² = 500
    Σ(yi - ybar)² = 800 (total sum of squares, SST))
    Σ(ŷ - ybar)² = 400 (total sum of estimators, SSE)
    Σ(xi - x̄)²(yi) = 200
    Σ(xi - x̄)²(εi) = 0
    n = 1000
    s² = 4

    3. The attempt at a solution

    R² = SSE/SST = 400/800 = 200

    But to be honest, I have no idea how to find β1, β0, or the variance of β... Can anyone help?
     
  2. jcsd
  3. Oct 4, 2014 #2

    RUber

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    Homework Helper

    Normally, in a regression equation like this, ##\beta_0 = \mu ## which is the overall sample mean. I don't see any immediately discernible information for finding those parameters, but it maybe in there with some algebra.
    Your ##R^2## equation looks right, but that is not equal to 200. ##R^2## is always between 0 and 1.
     
  4. Oct 4, 2014 #3

    SteamKing

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    Since when is 400 / 800 = 200? Is this the New Math everyone keeps talking about?
     
  5. Oct 4, 2014 #4

    939

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    lol yea stupid error, 0.5, sorry :(
     
  6. Oct 4, 2014 #5

    WWGD

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    Most statistical packages will spit out all the estimators if you input relatively little data.

    This Wiki page has explicit formulas for ##\beta ## and ## \beta_0 ##:

    http://en.wikipedia.org/wiki/Simple_linear_regression
     
    Last edited: Oct 4, 2014
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