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

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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[@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 ?

[@mingsiu9936]

this is 100000 times more useful than attending lectures

[@007nice3]

Why

[@ALV57]

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.

[@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.

[@alghamdiosamah9872]

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

[@meganmagnuson1930]

Thank you for the tutorials. My text book truly does suck and your tutorials are saving me in my online course. Very clear, concise and simple. This non-math minded person greatly appreciates them.

[@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

[@statisticsfun]

I would appreciate you sharing these with your friends and colleagues. This helps me get the word out about the educational videos. If you have not done so, make sure you like MyBookSucks on FaceBook (see link in video description). This will help me spread the word about the free videos.

[@m.d.332]

these tutorials make my day.It helps me understand statistics in a easy way.thanks a lot

[@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]

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

[@alexvech]

short, clear and straightforward ! keep going mate !

[@yanavanina9754]

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[@statisticsfun]

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

[@AshiPongener]

Party more study less is what 'm doing because of your videos! Inspiring!!! :) Ty

[@CryptoFinanceIQ]

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

[@kailene5430]

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

[@deliadykes6892]

wonderful! Happy Holidays!

[@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?

[@WorldThinker09]

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

[@rapunzelcorner]

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?

[@faridhuseynov9185]

Excellent tutorials. Thank you for clear explanations !

[@shoebshaon9935]

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

[@Strongest_Bear]

thank you it was simple and saved alot of time

[@sichonechanda9412]

Thanks Sir, you the best. Youve really helped me out. God bless

[@statisticsfun]

thank you!

[@dimitrismavridis2179]

Indeed, your explanation is great!

[@NeBueR4U]

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

[@tymothylim6550]

Thank you very much for this video :) It was very helpful and educational!

[@vmehighlow4481]

Thanks for the clear explanation, Helped me a lot!

[@mintoo2cool]

the link annotation to the playlist did not work for me. could you please verify that and correct it if necessary. i am on chrome if that helps at all. the video tutorials are amazingly calming and simple. i clearly know what to do. but i wish you'd spend some time giving the insight as to why these formulas are the way they are and why do they explain the quality of fit

[@yuny6717]

Hello sir, thanks for the information. however, would you mind explaining you obtain the estimated values, 2.8, 3.4, 4,4.6, and 5.2? please?

[@MrVirtualAI]

very nice and easy to understand....great thanks...!

[@fakhrulparvez]

Really very useful..... would you please make a video about OLS .... how to apply it

[@shekhar1180]

While calculating standard error of the estimate, what is the mathematical logic if any for deducting 2 from n in the denominator? I am trying to understand significance of the particular number 2... why 2 and why not 1 or even 0?

[@rshabbir7]

Thank you so much , truly

[@merciadios5113]

Hi, it seems like the links in your description are broken!

[@samwoon1947]

I enjoy hearing your voice , it sounds so nice (steadfast). hahaha Your videos are great I always listened to it. But for the video on standard error of estimate If the answer 0.89 then is it good? How do you benchmark? The lower the answer is more accurate? But how do you benchmark with what value? E.g 100% (1.0) is the max? Hope you can advise . Thanks a lot:)

[@jaybee2329]

what does 2 in the denominator represent?

[@anuradhapatel6077]

What is standard value for standards error for regressive

[@sum1sw]

What I have error in all variables? Would the standard error still be the square root of the sum of the square error /N-2? How do I calculate the standard error in the estimated parameters?

[@ratul7430]

I wonder, where is he now.

[@zacc58]

Thank you so much

[@nischalkc-q3o]

the video was greate but can u define what does that answer 0.89 mean to say

[@msabbour84]

you are simply perfect :)

[@vigilhammer]

thanks a lot

[@sumandhas6196]

what if the value of b1 is in negative

[@afifkhaja]

100%! Good job

[@nehakoli5086]

Can we calculate actual Value - estimated value?

[@limgraw5126]

hi and good evening.... may i know the reason why u prefer 'n-2' as ur denominator? i was confused with either to use 'N' or 'n-2'... ='(

[@statisticsfun]

Lim Graw typical n is used for a sample and N is for a population. In this case it does not really matter because there are just a few observations. Make sense?

[@limliang8282]

statisticsfun so it is okay for us to use 'n-2' for a few samples/observations, right?

[@solidaligator1527]

+statisticsfun why is 'n-2' used in this case? In order to maginify the degree of accuracy error? If not, then I fail to see why it can't be just 'n'. If the the purpose of the 'n-2' is indeed to magnify the accuracy error, then what is the rule of thumb when it comes to very large data sets, i.e. millions if not billions? Something in the order of: 'n-(n*0.1)'? Thanks.

[@nonsensepoopypants7415]

Anybody know what program he's using to make these videos?

[@statisticsfun]

That is what I am talking about! "Party More Study Less!!!!"

[@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."

[@MicroBugs]

thank you!

[@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]

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.

[@thehokipoki]

After watching your videos I'm finally learning how to do this and pass my class. Thanks so much!

[@statisticsfun]

Thank you!

[@samreens3365]

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

[@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)

[@Coreyrob26]

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.

[@tommy9x]

But you didn't say how Standard Error is good enough

[@statisticsfun]

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

[@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.

[@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.

[@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 :).

[@azamatkarimov693]

Thanks Allah you were sent to help us . Thank you very much it is much easier with you . never stop making outstanding videos and we will never stop liking it

[@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.

[@robbiedeegan3121]

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

[@raevim7586]

yes!! esp now that we have ol class

[@bluemesa5341]

+statisticsfun Could you please explain why we have to subtract 2 from number of observations 2:45. I know it's based on a derivation, but there should be reason behind it. Appreciate your help. Thank you!

[@statisticsfun]

Bubble gummah... since you are squaring it does not matter if it is y - y hat or y hat - y. Because squaring gets rid of the negative signs.

[@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.

[@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.

[@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]

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.

[@osamamelhem]

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

[@statisticsfun]

Thank you and I appreciate the feedback. Make sure you like MyBookSucks on Facebook (see link in video description). This will help others find the educational videos.

[@statisticsfun]

Aren't you sweet! Make sure you give me some love on FaceBook and Like MyBookSucks (see link in video description). This will help others find the educational videos and fall in love with me too.

[@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.

[@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.

[@zeeshanqasim8925]

Thank you, sir, for your gorgeous services. I will appreciate if you please make a video of the drawing and understanding the box plots that are ubiquitous in research articles.

[@statisticsfun]

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

[@statisticsfun]

Great to hear and thanks for the video back. I have thought for sometime now that animation is the way to teach.

[@hendrikl2906]

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

[@REPATHATHYALA]

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

[@emanuel5109]

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

[@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]

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

[@daxdasche6112]

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.

[@statisticsfun]

Wonderful that you are catching on to statistics.

[@thecodinggamer5378]

I got stuck ? I understood until you said , estimated value minus the original value, but why did you squared the equation??? I am facing the same problem in machine learning course , please reply

[@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!

[@majnejati]

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

[@mounirfazzaa4767]

If we were using a quadratic form instead of a linear one, should we put N-3 in the denominator since we would have to estimate 3 constants a, b and c?

[@CPZarolawala]

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

[@KiranSharma-kc2sk]

Most of equation show it to devide value by (n), not with (n-2), like this video to understand (y)

[@ashishdhungana633]

Why do we use (n-2) in denominator in the formula. Can't we use (n-1) instead?

[@ritamart9041]

The excel function STEYX returns the standard error just for linear regressions right?

[@mohammedelqadmiry2999]

but what happen if i have the points at 0 5 10 15 25... rather than 1 2 3 4 5...?

[@EllismoreCA]

I really don't understand the difference between this and r^2.

[@kiwifruitkl]

I didn't mean to refer to romantic or erotic love. It was a misleading comment. I intended to refer "you" to the video, not the person making the video, thereby personifying the video as a person and showing overwhelming gratitude to the video.

[@dannyninhio]

Hi there, i have calculated the standard error of the estimate for my regression and how would i interpret it in comparison to the predicted value? The standard error of the estimate being 8.82 and the predicted value from the regression equation being 14.220

[@vigneshcs3162]

Is standard error or error terms are similar? What about random error and residuals?? Please upload a video on these types of errors!

[@wilhougby]

Why do we divide it by n-2?

[@KashifMaqsood1]

wilhougby please search videos for 'degrees of freedom'

[@yaliimvp]

I have the same question because usually I do it as n-1. Where does the 2 comes from?

[@sahilbhatia8051]

The degrees of freedom in a linear regression are n - k - 1 where k is the number of explanatory variables / predictors; here there is only 1 predictor, so df = n - 2