Standard Error of the Estimate used in Regression Analysis (Mean Square Error)
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- Опубликовано: 4 фев 2012
- An example of how to calculate the standard error of the estimate (Mean Square Error) used in simple linear regression analysis. This typically taught in statistics.
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x2
Great question! It is "degrees of freedom" or df. The reason we use 2 is because we have 2 variables (x and y) in this case. If we had more than 2 variables like x, y, and z the df would be n-3.
In an earlier video I show how the regression line is forced through the point where the mean of x and y intersect. These "2" points are not included in the "average of the errors" because the error at these 2 points is 0.
I need to create a video on d.f. for sure.
Awesome!
Thank you for this awesome video! I feel we should divide R2 by (n-1) and divide the standard-error-of-the-estimate by n.
R2 uses an average y value from the sample. However, this average y value in the sample might not be the same as the average y value in the whole dataset. Thus, we have to divide R2 by (n-1). Here is the detailed explanation: stats.stackexchange.com/a/87422/318006
For the standard-error-of-the-estimate, since we do not use the average value from the sample, it might not be necessary to divide it by (n-1) or (n-2)
@statisticsfun Can you please explain what's the difference between RMSE and Residual standard error (RSE) ?? We are diving by N for RMSE which gives baised estimate of deviation due to which we are dividing by degrees of freedom . Is that correct ? If yes , Is it better to use RSE in all cases instead of RMSE ?
Thank you for the feedback, much appreciated.
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Every stat student should have to watch something like this so they can understand why they shouldn't be intimidated learning this stuff. You did an excellent job with this series of videos, thank you so much.
May I just say sir that you are marvellous at this. Your explanation style, calm voice, uncluttered wording, steady pace to let it sink in, all works so well for me, and it seems from below, others too. Well done.
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The link to the playlist on regression is in the video description (of this video). RUclips does not allow me to add links in comments.
After watching your videos I'm finally learning how to do this and pass my class. Thanks so much!
Bridgette, yes I do. This video is part of a larger playlist. If will see a link to the entire playlist in the video description. In the second video I discuss how to calculate all the coefficients.
Awesome explanation. My instructor was impossible to follow but you made this very clear and showed how simple it really is. I learned more in the first 3 minutes of this video than I did in the whole hour of my class.
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You are very welcome (remember this channel is call Statisticsfun). Make sure you like MyBookSucks on Facebook (see video description for link). This will help others find the educational videos.
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Thanks for pointing that out. I added a link in the video description to the playlist. Hopefully the playlist can give you more insight into the nature of the formula's especially the first video.
I appreciate your feedback too because the pace and detail of the videos is always a struggle for me. Good luck on your classes too.
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Why -2 in denominator i.e. n-2, why not some else number
@@priyandumbajpayee4398 "Great question! It is "degrees of freedom" or df. The reason we use 2 is because we have 2 variables (x and y) in this case. If we had more than 2 variables like x, y, and z the df would be n-3."
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Thank you for making this. 8+ years later and still helping others (like myself) understand stats
yes!! esp now that we have ol class
Such an amazing Simplification..I am learning machine learning and I have to start building machine models but I didn't how regression line was being calculated. You made it so clear for me. Kudos to you brother.
great video, I'm been searching all over trying to figure out all plots on a straight line and it's standard error of estimate. You didn't even tell us and I figured it out :) Thanks so much.
@Norfeldt Very good question. The reason is we are estimating two variables b1 and b0. The larger the sample size the less impact this subtracting two will have.
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Im at working trying to dig this stuff out of my brain from my old statistics class no one has been able to help. 1:30 into this video and I got it down. Thank you
I am really very thankful to you for such a very good explanation. I would recommend these lectures to others to clear their basics. Now I am going to see all videos with the relevant topics on youtube. Please let me know if you have more and other topics on logistics regression and other regression models used in financial and statistical modeling. Thanks and Regards - Chirag Patel
Thank you and is always good to hear the videos are helpful and informative.
You will see R2 (r squared) most of the time and in fact there is a strong relationship between R2 (r squared) and standard error of the estimate.
Thanks for clarifying the difference between R squared and Mean Squared Error. Great video!
Wonderful that you are catching on to statistics.
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Great to hear and thanks for the video back. I have thought for sometime now that animation is the way to teach.
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@skibumanne Typically both the standard error of the estimate and R^2 are used. Of course if R^2 = 1, standard error of the estimate (SE) would be 0. They both tell us how good of fit, but R^2 tells us a bit more. For example an R^2 of .45 means the regression explains about 45% can be explained by the linear relationship. You would use the SE if you were going to show the upper and lower bounds (or interval of the regression line).
Good to know about the m and b too -- thanks.
The color coding and animations are really helpful!
Very good to hear. Make sure you like MyBookSucks on FaceBook (see link in video description). This will help me spread the word about the videos.
Precise, to-the-point ! Loved it..
Yes I believe the MMSE (minimum mean square estimate) is the same thing as least squares used in linear regression.
The standard error of estimate is very similar to the standard deviation. So comparing standard error the estimate is similar to comparing the standard deviation and the mean. In the case of a regression you have a lot of means (or actual values).
You would want to compare 14.220 to the actual predicated value at that point as well. Keep in mind the standard error of the estimate is the "average error" not the specific error rate.
Hope that helps.
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Thanks for pointing that out. I had a typo in the link that I have corrected now.
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Megan Magnuson Megan, thank you so much for taking the time to write me -- it is much appreciated. If you get a chance like, share the videos. It helps get the word out. Liking our FB page helps too. www.FaceBook.Com/PartyMoreStudyLess
The Standard Error of the Slope is what you are trying to find. You take the standard error of the estimate divided by sum of the differences of the x values squared.
Sb1=Syx/Square Root(SSX)
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The short answer is this is degrees of freedom, the reason 2 is used is because there are two variables estimated. The y intercept and the coefficient of the independent variable or slope of line. As the number of observations increase this n-2 adjustment becomes less and less important.
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Thank you very much your tutorial is very useful and things become much easier when I watched your video series.
Thank you! Simple and easy to understand example.
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Very good video; easy to understand and takes step by step / slow
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Thank you excellent job of explaining. Broke it down so it was easily understandable.
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Thank you for this video! It was clear and easy to comprehend. Can you explain how the standard error of the estimate has a direct relationship with the SD of the criterion and an indirect relationship with validity?
Honestly, you teach better than most lecturers. You should have more subscribers 👍. Just one question, in what situation would you use the regression line?
Thanks a lot for this straightforward tutorial video!
You really make Stats fun, lots of fun. Thank you :-)
@Norfeldt That is good information for me to know, btw, what country do you live in?
@statisticsfun Thank you once again for the reply. In my country we normally use "a" as the slope and "b" as the interception which is why i didn't recognized it. I'm all set with your answer and looking forward to your next video :-)
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I know! I was just joking around as well. I do appreciate the comment and I understood it perfectly.
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@Norfeldt The b0 is the y intercept and b1 is the slope of the line. If you had three variables (x, y, and z), then you would have n-3. And Yes, it does have to do with the degrees of freedom.
Degrees of freedom are the number of variables that are "free to vary." As samples sizes get large there is less of an impact of this goofy denominator.
Very well explained, thanks so much.
Thank you very much, it is good explanation to understand the regression analysis
to apply for error estimation.
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Very nice explanation sir...
You helped me explain standard error in my report for university thanks
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Sir what is r2 after 3.20 what u did??kindly explain
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Thank you for the Regression Analysis series of videos. Please help with doing regression analysis on Cryptocurrency as well.
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