# Thread: Standard Error of Coefficient w/1 Independent Variable

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

The denominator for SE(lstat) should be rather than SSR.

However, note that .

So substitute in the right amounts and you should arrive at the answer.

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

Thanks so much!!!!!!

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