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SER vs. standard error of the estimate

fullofquestions

New Member
Perhaps someone can clarify. I have seen the following two equations that I thought were for the same quantity but I am not sure. These relate to the 'Standard Error of the Regression' and 'Standard Error of the Estimate.'

SER is defined as SQRT(RSS/n-2) [by the way, the following topic clarifies the degrees of freedom: ]http://www.bionicturtle.com/forum/viewthread/1518/]

RSS is given as: Summation (Yi - Ybar)^2


Now, I've seen the equation for 'Standard Error of the estimate' as sigma / SQRT(n)

These two must be different since RSS isn't the same a variance. Can someone please explain?

Much appreciated.
 

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Right, "old" SEE = new SER

Summation (Yi - Ybar)^2: please tell me if i have that somewhere, that's wrong: RSS = sum of residuals squared, so observation (Yi) minus predicted or estimated (Y carrot)

Re: "Now, I’ve seen the equation for ‘Standard Error of the estimate’ as sigma / SQRT(n)"
No, please don't use this, now we are confusing standard errors

standard error of sample mean = sigma / SQRT(n); this is CLT, no regression needed
standard error of regression = SER = SQRT(RSS/d.f.); this is standard deviation of predicted/estimated Y in a regression
standard error of regression coeffiecient = e.g., SE(b1); you won't need to calculate

David
 
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