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# Standard deviation of residuals or root mean square deviation (RMSD)

Standard deviation of the residuals are a measure of how well a regression line fits the data. It is also known as root mean square deviation or root mean square error.

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• In the video on the same topic of the Statistics and Probability course (https://www.khanacademy.org/math/statistics-probability/describing-relationships-quantitative-data/assessing-the-fit-in-least-squares-regression/v/standard-deviation-of-residuals-or-root-mean-square-error-rmsd), Sal asks us to divide by n-1 (instead of n-2). Could anyone explain what is the difference between the two examples ? I suppose in both cases, we are talking about a sample (statistics) instead of the population (parameter) and hence n should not be used ? Many thanks.
• At the end of the video, Sal mentions about the significance of RMSD; we can treat it like "average prediction error between [the] points."

I am confused. We call it Standard Deviation of residuals. The name sounds like it's going to tell us about how spread the residuals are. However, the formula quite looks like root square mean of residuals which tells us about the average prediction error between the points.
• Did Sal square the sum of the residuals?
• First, he squared each residual individually and then he summed them up.
• Why in the other stats course on this site is RMSD calculated using n-1 in the denominator but here it is calculated using n-2?
• I understand the concept and how to do the problems, but what is the point of squaring the residual in general? To go off of that idea, I also don't understand why you can't just do the "regression line of best fit" instead of calling it the "least squares" regression.

Basically, why is anything being squared? Thanks!
• We square everything to essentially get rid of negative values. Otherwise we wouldn't get a "TRUE" idea of how far spread our data is. Think about it, if we have negative differences we will end up with a smaller difference from the regression line. Reducing the difference from our line of best fit.
• How do I change mi avatar.
(1 vote)
• you go to your asinments and click on your charcter and sat all avatar
(1 vote)
• What's the point of finding the standard deviation of the residuals?

Is it a measure of how spread out the data points are from the line, a lower number for which would indicate a tighter fit to the regression line?

Edit: Nevermind, got the answer loll
(1 vote)
• How can you solve this on a TI84 Plus?
(1 vote)
• Would we be provided this formula on the AP test, or would we not even need it?
(1 vote)
• For the answer Sal got at , shouldn't it be (sqrt(3)/sqrt(2)) instead of (sqrt(3)/2)