Standard Error of the Estimate used in Regression Analysis (Mean Square Error)

[@indian_street_view]

You made this so simple, even non mathematical background students can understand this. You have no idea how your videos helping me in my career. I can't thank you enough for this

[@quelesvalgareata1838]

x2

[@statisticsfun]

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.

[@prathameshpradipdatar2003]

Awesome!

[@DL-rw1fw]

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)

[@modemnaveen6240]

@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 ?

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[@007nice3]

Why

[@NivethRichard]

Not one to comment on Videos in YT. But you deserve it. You distilled the regression topic to its essence while keeping it absolutely simple. Thank you!

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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.

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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.

[@thehokipoki]

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[@saad4q]

Wow, the simplest and most straightforward way to explain Regression. This is better than everything I've read and seen.

[@limitationsoflanguage]

Of about four videos I tried to watch on this subject yours was by far the most well done and easy to understand - thank you!

[@hendrikl2906]

this guy explains in 3 minutes what a teacher can't in 1.5 hours. Thank you!

[@robbiedeegan3121]

Thank you for making this. 8+ years later and still helping others (like myself) understand stats

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[@faadi4536]

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.

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[@statisticsfun]

@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.

[@statisticsfun]

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.

[@alghamdiosamah9872]

Thank my professor Dr. David, you make the statistic more fun for me. I never forget your amazing teaching at Avila University

[@statisticsfun]

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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[@meganmagnuson1930]

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[@statisticsfun]

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

[@ronniegirl69]

Thank You so much, I've been struggling with this chapter, and getting behind in class, because, I couldn't move one until I figured this out. With your awesome video, I got it!!!!!! Excellent Teacher!!!!

[@statisticsfun]

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.

[@statisticsfun]

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)

[@m.d.332]

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[@statisticsfun]

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[@priyandumbajpayee4398]

Why -2 in denominator i.e. n-2, why not some else number

[@TricksticKx]

@@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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[@statisticsfun]

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. Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

[@statisticsfun]

Wonderful that you are catching on to statistics.

[@mitchellmeyer4177]

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

[@statisticsfun]

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.

[@emanuel5109]

Thanks for clarifying the difference between R squared and Mean Squared Error. Great video!

[@statisticsfun]

Yes I believe the MMSE (minimum mean square estimate) is the same thing as least squares used in linear regression.

[@somu9083]

best video for understanding, before this I could not understand for one semester now it is clear in 10 minutes

[@elizabethhankammer5698]

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[@statisticsfun]

***** You are very welcome. Good luck in your studies too.

[@vsadha5241]

@@statisticsfun negative values how to avoid sir in linear regression

[@statisticsfun]

@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.

[@ocayaro]

You speak clearly and slowly. Your slides are well augmented with illustrations. Thanks for this refresher.

[@harunsuaidi7349]

The color coding and animations are really helpful!

[@danil.torresashbridge1119]

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.

[@alexvech]

short, clear and straightforward ! keep going mate !

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[@statisticsfun]

@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.

[@statisticsfun]

Thank you and is always good to hear the videos are helpful and informative.

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BEST! I cannot thank you enough. I'll be studying in the next semester but for research paper, I needed to understand it well, and you take all the credits :D

[@statisticsfun]

I know! I was just joking around as well. I do appreciate the comment and I understood it perfectly.

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[@bazas450]

Honestly, you teach better than most lecturers. You should have more subscribers 👍. Just one question, in what situation would you use the regression line?

[@CPZarolawala]

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[@statisticsfun]

Thanks for pointing that out. I had a typo in the link that I have corrected now.

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[@avrrao1940]

Very good presentation - clear and simplified. Thank you.

[@statisticsfun]

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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[@Norfeldt]

@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 :-)

[@Challenze]

Thank you! Simple and easy to understand example.

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[@skibumanne]

wow, thanks so much for your quick and understandable response! It's been my goal for years to learn this and understanding it is so very rewarding.

[@statisticsfun]

The link to the playlist on regression is in the video description (of this video). KZbin does not allow me to add links in comments.

[@CryptoFinanceIQ]

You helped me explain standard error in my report for university thanks

[@statisticsfun]

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.

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Precise, to-the-point ! Loved it..

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best tutorial i've ever seen... thanks a lot.. what best method should i use if i need to find the relationship between two variables?

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[@statisticsfun]

@Norfeldt That is good information for me to know, btw, what country do you live in?

[@osamamelhem]

Thanks so much for the clear video. What is the equation of the standard error of the mean? Thanks in advance.

[@statisticsfun]

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.

[@Sunshine-zi7oy]

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[@lonelyjokers4]

learned way more watching your playlist than in have in actual class

[@kailene5430]

Thank you excellent job of explaining. Broke it down so it was easily understandable.

[@faridhuseynov9185]

Excellent tutorials. Thank you for clear explanations !

[@majnejati]

Thanks for the detailed explanation. May I ask why the degree of freedom for this is -2 ? like instead of -1 ?

[@lawrence2467]

Thanks a lot for this straightforward tutorial video!

[@statisticsfun]

Thank you!

[@samreens3365]

Sir what is r2 after 3.20 what u did??kindly explain

[@statisticsfun]

Thank you for the feedback, much appreciated. Make sure you like MyBookSucks on FaceBook (see link in video description). This will help other students find the educational videos and help them "see" too :).

[@sharayu8876]

Thank you for video! It was very helpful but can you please also share link/playlist to Regression analysis from first using the least square method? Also what’s is scatter plot in regression??

[@emilyedwards4841]

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?

[@REPATHATHYALA]

this is super... sir... really fantastic... very clear and upto near perfection... where r square is 0.999999999

[@chalenegirl1]

Conceptually, when would you use R2 instead of standard error of the estimate? I see how they are different but is one "better" than the other? These are very good videos. Thank you for all of these.

[@dimitrismavridis2179]

Indeed, your explanation is great!

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[@statisticsfun]

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Awesome video!! very very helpful. Today is my quiz and you saved me sir

[@ranyael-shirbini8600]

Hi, thanks for these videos they are so easy to follow! Just wanted to ask if its the estimated value-actual value or actual value-estimated value. In my text book its actual value -estimated value, or they show it as Square root of SSE/n-2. Thanks again!

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wonderful! Happy Holidays!

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This is how you should teach a student. Thanks

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Very well explained, thanks so much.

[@NeBueR4U]

Thank you for the Regression Analysis series of videos. Please help with doing regression analysis on Cryptocurrency as well.

[@vmehighlow4481]

Thanks for the clear explanation, Helped me a lot!

[@WorldThinker09]

Thank you very much, it is good explanation to understand the regression analysis to apply for error estimation.