# Thread: Standard Error of the Residuals

1. ## Standard Error of the Residuals

Hello,

Iknow that the standard error of the residuals of a regression equation is given as the sqare root of SSE divided by the degrees of freedom and its interpretation is that it is the average deviation of each value of Y around around the estimated Y values from the line.

However i have seen that there is another st error of the residuals that correspond to each one of the observations of the regression. So if we have a regression with 30 obs this variable standard error is calculated 30 times (SAS output this standard error). Its formula is SE = Sqrt[MSE*(1+Hat_i)]
What is the interpretation of this variable standard error and what is its relation with the standard error that i describes at the beggining of this thread?

Thanks,

ANdreas

2. If you look at your SAS /r output, starting at the left:

'Dependent Variable' is the raw dependent variable data (Y).

'Predicted Value' is the predicted value using the fitted line (Y^).

'Std Error Mean Predict' is the Standard error used for confidence Intervals.

'Residual' is the difference between the first two above (Y-Y^).

'Std Error Residual' is the standard deviation of the 'Residual' statistic. Used like other standard errors.

'Student Residual' is the standardized residual. Calculated as 'Residual' / 'Std Error Residual'. Consider these as Z scores. This may help you with your question(?).

'-2 -1 0 1 2' is a graph of 'Student Residual'.

'Cook's D' is a measure of influence. This estimates an observation's influence by adjusting residuals when omitting that observation from the model.

Hope that helps.

3. ## Re: Standard Error of the Residuals

This is a new question related to residual standard error

Can the residual standard error be used to determine whether the model fits well?

Thanks

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