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Thread: Standard Error of Coefficient w/1 Independent Variable

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    Standard Error of Coefficient w/1 Independent Variable




    Hi-

    I'm studying regression via ISLR and trying to manually calc a standard error for a data set to better understand the intuition. Below is my R regression output:

    Residuals:
    Min 1Q Median 3Q Max
    -15.168 -3.990 -1.318 2.034 24.500

    Coefficients:
    Estimate Std. Error t value Pr(>|t|)
    (Intercept) 34.55384 0.56263 61.41 <2e-16 ***
    lstat -0.95005 0.03873 -24.53 <2e-16 ***
    ---
    Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1

    Residual standard error: 6.216 on 504 degrees of freedom
    Multiple R-squared: 0.5441, Adjusted R-squared: 0.5432
    F-statistic: 601.6 on 1 and 504 DF, p-value: < 2.2e-16

    RSE per =6.216
    Sum of Squared Variances of variable lstat=25,712 (calc'd in excel)

    SE (lstat)= RSE/SSR(predictor); Therefore SE(lstat) =6.216/25,712 ==.00241

    BUT the R output (above) says it's .03873 . Where did I go wrong?

  2. #2
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    Re: Standard Error of Coefficient w/1 Independent Variable

    The denominator for SE(lstat) should be \sqrt { \sum { { \left( x_{ i }-\overline { x }  \right)  }^{ 2 } }  } rather than SSR.

    However, note that SSR = { \hat { \beta } }_{ 1 }^{  2} \sum { { \left( x_{ i }-\overline { x }  \right)  }^{ 2 } }.

    So substitute in the right amounts and you should arrive at the answer.
    http://ab-stats.com

  3. #3
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    Re: Standard Error of Coefficient w/1 Independent Variable


    Thanks so much!!!!!!

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