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use "." rather than "," for decimal separator, as this is an English language site

edited Oct 13, 2015 at 21:45

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Say we have the following ANOVA table (adapted from R's example(aov) command):

 Df Sum Sq Mean Sq F value Pr(>F) Model 1 37.0 37.00 0.483 0.525 Residuals 4 306.3 76.57

If you divide the sum of squares from any source of variation (model or residuals) by its respective degrees of freedom, you get the mean square. Particularly for the residuals:

$$ \frac{306.3}{4} = 76.575 \approx 76.57 $$

So 76,.57 is the mean square of the residuals, i.e., the amount of residual (after applying the model) variation on your response variable.

The residual standard error you've asked about is nothing more than the positive square root of the mean square error. In my example, the residual standard error would be equal to $\sqrt{76,57}$$\sqrt{76.57}$, or approximately 8,.75. R would output this information as "8,.75 on 4 degrees of freedom".

Say we have the following ANOVA table (adapted from R's example(aov) command):

 Df Sum Sq Mean Sq F value Pr(>F) Model 1 37.0 37.00 0.483 0.525 Residuals 4 306.3 76.57

If you divide the sum of squares from any source of variation (model or residuals) by its respective degrees of freedom, you get the mean square. Particularly for the residuals:

$$ \frac{306.3}{4} = 76.575 \approx 76.57 $$

So 76,57 is the mean square of the residuals, i.e., the amount of residual (after applying the model) variation on your response variable.

The residual standard error you've asked about is nothing more than the positive square root of the mean square error. In my example, the residual standard error would be equal to $\sqrt{76,57}$, or approximately 8,75. R would output this information as "8,75 on 4 degrees of freedom".

Say we have the following ANOVA table (adapted from R's example(aov) command):

 Df Sum Sq Mean Sq F value Pr(>F) Model 1 37.0 37.00 0.483 0.525 Residuals 4 306.3 76.57

If you divide the sum of squares from any source of variation (model or residuals) by its respective degrees of freedom, you get the mean square. Particularly for the residuals:

$$ \frac{306.3}{4} = 76.575 \approx 76.57 $$

So 76.57 is the mean square of the residuals, i.e., the amount of residual (after applying the model) variation on your response variable.

The residual standard error you've asked about is nothing more than the positive square root of the mean square error. In my example, the residual standard error would be equal to $\sqrt{76.57}$, or approximately 8.75. R would output this information as "8.75 on 4 degrees of freedom".

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answered Oct 13, 2015 at 15:12

Waldir Leoncio

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Say we have the following ANOVA table (adapted from R's example(aov) command):

 Df Sum Sq Mean Sq F value Pr(>F) Model 1 37.0 37.00 0.483 0.525 Residuals 4 306.3 76.57

If you divide the sum of squares from any source of variation (model or residuals) by its respective degrees of freedom, you get the mean square. Particularly for the residuals:

$$ \frac{306.3}{4} = 76.575 \approx 76.57 $$

So 76,57 is the mean square of the residuals, i.e., the amount of residual (after applying the model) variation on your response variable.

The residual standard error you've asked about is nothing more than the positive square root of the mean square error. In my example, the residual standard error would be equal to $\sqrt{76,57}$, or approximately 8,75. R would output this information as "8,75 on 4 degrees of freedom".