Logistic Regression Details Pt1: Coefficients

When you do logistic regression you have to make sense of the coefficients. These are based on the log(odds) and log(odds ratio), but, to be honest, the easiest way to make sense of these are through examples. In this StatQuest, I walk you though two Logistic Regression Examples, step-by-step, and show you exactly how the coefficients are derived and how to interpret them.
NOTE: This StatQuest assumes that you are already familiar with...
The main ideas of Logistic Regression: • StatQuest: Logistic Re...
Odds and Log(odds): • Odds and Log(Odds), Cl...
Odds Ratio and Log(odds ratio): • Odds Ratios and Log(Od...
Linear Regression: • The Main Ideas of Fitt... and
Linear Models: • Linear Regression, Cle...
• Using Linear Models fo...
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0:00 Awesome song and introduction
1:13 Review of Logistic Regression Concepts
2:47 Coefficients for continuous variables
10:46 Coefficients for discrete variables
17:52 Coefficients for combinations of variable types
Correction:
15:21 The left hand side of the equation should be “log(odds Obesity)” instead of “size”.
#statquest #logistic

[@statquest]

Correction: 15:21 The left hand side of the equation should be “log(odds Obesity)” instead of “size”. NOTE: In statistics, machine learning and most programming languages, the default base for the log() function is 'e'. In other words, when I write, "log()", I mean "natural log()", or "ln()". Thus, the log to the base 'e' of 2.717 = 1. Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/

[@borispenaloza6788]

Josh.. thanks for these videos man.. one question did you mean obese = log(odds normal_gene) x B1 + ... instead of size = log(...???

[@statquest]

@@borispenaloza6788 What time point in the video (minutes and seconds) are you talking about?

[@borispenaloza6788]

@@statquest Starting at 15:23.. you mentioned obesity but the equation shows size...

[@statquest]

@@borispenaloza6788 Ahh, I see. That's a typo.

[@borispenaloza6788]

@@statquest yes.. but it was a great explanation!

[@kuntalnr]

I am very emotional when writing this. I was struggling to learn logistic regression until I came to this channel and it has really transformed my understanding and confidence. I love how this channel uses visual tools and graphs to explain the concepts instead of some heavy dose of equations. This channel is a blessing to students like us who struggled during pandemic with classes.

[@statquest]

Hooray! I'm glad the video was helpful! :)

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Thi is sooooo true, this channel is a bless for students like us and the way your r explaining with practical example is like I've found my heaven. Many many thanks for these videos. You are one of my best teacher in stats.

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[@statquest]

Wow! Good luck!

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yea man, I took biostats three times in my life (undergrad, masters, PhD) and the only time things REALLY made sense at the intuitive level is watching StatQuest explanations.

[@Anonymous-54545]

@@MrSpiritmonger I have a graduate degree in pure math and I'm on here watching these so I can learn how to succinctly summarize things to my nontechnical boss (in this case I actually don't know the concept at all and this time it's for me, but that's how I found the channel)

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Saaame!

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How was it?

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You're an absolute gem of human being. It takes a special talent and surely a lot of work to be able to explain these concepts so clearly ! Thank you so much for sharing all of this with us :)

[@statquest]

Thank you very much! I really appreciate your support - it means a lot to me. :)

[@kritisk1]

Josh, ur my stats savior. Everyone start teaching very serious "let's get to the topic" but u soothe us with that gentle guitar beat and make us feel so comfortable. I just don't know how to express my gratitude, still thanks a ton and I mean it

[@statquest]

Thank you very much! :)

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Can’t believe I’m saying this. Right after I finished watching a video of someone doing fancy snowboarding tricks, I started binge-watching your statquest videos and I got so addictive... I started hating stats for the last term because of a boring prof but you saved my butts!!!

[@statquest]

BAM! :)

[@mostinho7]

4:50 in linear regression, y axis can have any value (which makes it easier to solve) but for logistic regression y values confined between 0 and 1 as it represents the probability. To deal with this, we transform the y axis to be log odds instead of probability Transforming probability to log odds using the logit function, logit = log(p/(1-p)) 5:50 how the axis changes The old y axis (in probability) that went from 0.5 to 1 goes to 0 to infinity (in log odds) 8:00 the log odds y axis transforms the curved plot to a linear plot 8:20 the coefficients of logistic regression are for the linear plot of log odds axis 8:48 you get coefficients of the kind just like linear regression 9:30 don’t understand, check odds ratio stat quest

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Thank you! :)

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[@statquest]

Thank you! I'm glad my videos are so helpful. :)

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[@statquest]

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Hooray!!! I'm glad you like this video so much! :)

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Absolute Stunner! I sat through hours of classroom lectures and mentoring yet couldn't understand it simple enough like you explained on this video. Thank you!

[@statquest]

Thank you very much! :)

[@alexz7432]

This is the best song I heard from watching your channel so far :D Anyway, your clear explanation is awesome. Keep up the great work!

[@statquest]

Thank you so much! :)

[@RaviShankar-jm1qw]

Could not resist joining your channel after seeing this video. Damn, you are genius Josh and indeed a blessing for people like us who get overwhelmed by Statistics due to the heavy theory prevailing everywhere. Absolutely loved the numbers approach which shows how the logistic regression is calculated!

[@statquest]

Thank you so much!!! I really appreciate your support. :)

[@miamyos]

Hi, I just wanted to say thank you for these videos. I have tried to help a friend with this for a while because her teacher isn't very good at explaining things and it's been hard because it's been almost a decade since I took a statistics course. Your videos are extremely helpful and your explanations are so good, I think both me and my friend have learned more in two videos than we have during the entirety of her course. Thank you ❤

[@statquest]

I'm glad my videos are helpful! :)

[@stats2econo]

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[@statquest]

Thank you very much! :)

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Thank you so much! Your clarity is brilliant! If all the teachers in the world explained like you, there wouldn't exist such a thing as bad students.

[@statquest]

Wow, thank you!

[@myip05]

kudos to you, not everyone learns the same, you show everything explicit and on simple terms. Thank you for doing this.

[@statquest]

Glad it was helpful!

[@tanbui7569]

Josh, your videos can never give me a break. Always have something new to note down. I've been practicing Logistic Reg and Deep Learning for a while but I never knew Logistic Reg is grounded in log(odds). I do not think any ML/DL books or courses actually cover log(odds), at least in all that i've read/studied. They only mentioned the activation function which is the sigmoid. Thank you for the awesome video as always.

[@statquest]

Thank you very much! :)

[@danieljohnson220]

i am currently doing a degree in Comp Sci and AI and am regularly referring to your videos as they explain the concepts so well. Really useful channel!

[@statquest]

Glad you like them!

[@younghoe6849]

Not easy to find a teacher who can explain in this way. Really talented teacher.

[@statquest]

Thank you very much! :)

[@rankzkate]

Am on a StatQuest Marathon.Addicted to this videos.Glad I found them. Asante sana.Much love from Kenya

[@statquest]

Wow! Thank you very much! :)

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I'm from Chile, and i just want to say you: YOU ARE AN AMAZING TEACHER, PERIOD!

[@statquest]

BAM! Thanks! :)

[@thej1091]

I was doing the DATA SCIENCE CAPSTONE COURSE on linear regression! horrible teaching! Man you killed it! I finally understand log odds and how it manifests as log odds ratio! thank You! Statquest! The comparison to linear regression! My god! Great stuff and Great teaching!

[@aryapranahutama6569]

I see why you made a wonderful video about statistics. It explained by the song in the beginning of this video!! You made it by joy and passion. Thanks so much for your videos

[@joseamaldonadomartinez480]

I learned a lot watching your logistic regression playlist! ! Thanks for making these videos!

[@statquest]

My pleasure!

[@jesusalbertoperezguerrero2560]

Thank you so much! You're one of the coolest and most talented teachers I've ever had!

[@statquest]

Wow, thank you!

[@nguyentruongaccacfa5538]

Hi Josh, I'm from Vietnam. I have read a lot of literature related to econometrics but it is only after watching this video that I really understand what maximum likelihood estimation is. This is really the pinnacle of Mathematics!

[@statquest]

Wow, thank you!

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thank you! you really are a great teacher, there is nothing like a teacher who can explain something in such a simple way!

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[@statquest]

Hooray! Thank you so much! :)

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I really love the text that displayed when you explained. I'm not good in English. Sometime I cannot catch up the word you said but I still clearly understand your explanation because of helping from that text. Thank you.

[@statquest]

Hooray! I'm glad you like the text. :)

[@hgr126]

Over the past couple months I have been self learning stats and data science and struggled a lot even though I genuinely loved learning about them. I am a visual learner so it was so hard to comprehend many simple concepts sometimes. I spend many hours a day on my own accord studying, and most of them are wasted on trying hard to understand a concept visually. Even though ChatGPT saved me a lot, they have so much trouble visualising concepts. Now I chanced upon your channel, I am just honestly dumbfounded by how visual your explanations and how good they are. Just speechless, and I just wanna leave a comment of appreciation. I sometimes feel proud of myself being able to visualise simple concepts myself, but those are nothing compared to your visualisations. This amount of visualisations especially for complex topics 1000% requires a certain talent and an extreme understanding of the concepts. Wishing for your continued success ahead

[@statquest]

Thank you very much and good luck with your studies!

[@hgr126]

​@@statquest Thanks! 2 days of watching several videos, I couldn't help it but decide to support you by just placing an order for your book from amazon today. :') ps: i genuinely dont buy books often, maybe once in every few years. That's how grateful i am. Thank you Josh

[@statquest]

@@hgr126 Awesome! Thank you very much for your support!

[@ranfuchs3592]

Brilliant and clear. Makes a relatively complex topic really simple. Thank you

[@statquest]

Thank you! :)

[@shrikantagrawal8239]

Triple Bam!!! Thanks a lot Josh.This really clears up a lot of confusions.

[@jiayiwu4101]

When I first watched your linear reg videos, I think they are not as good as probability videos. After I watched your linear + logistic reg videos, I know I was totally wrong. You link those two brilliant things together in such an easy and intuitive way. So BRILLIANT!!!

[@statquest]

Wow! Thank you very much! :)

[@jiayiwu4101]

@@statquest If you could add assumptions explanations about linear and/or logistic regression, that would be fantastic. A lot of interviews, from financial quant to tech industry, they love to ask those.....

[@mchakra]

Josh you're explanations are spot on!

[@statquest]

Thank you!

[@MichalJablonski-xe2ht]

Josh you are a teaching Rockstar the size of Walter Levin. Thank you so much! Just bought the book. Loving it!

[@statquest]

Thank you so much! :)

[@marcoventura9451]

Thank You for the beautiful and relaxing videos.

[@statquest]

TRIPLE BAM!!! Thank you so much for supporting StatQuest!!! :)

[@nurwani556]

Such a good, simple, clear video explanation!

[@statquest]

Thanks! :)

[@tallwaters9708]

Good man! It's easy to underestimate how much is in logistic regression.

[@statquest]

Thanks! :)

[@kunalramchurn4700]

Mr Statquest, you are the best sir!

[@statquest]

Wow, thanks!

[@hajer3335]

best explain ever. you have ability to make us so interested in stat. this channel is just my favorite. THANK YOU. i want to know if you have a book in this topic or an article?!

[@statquest]

Hooray! I'm so glad to here you like the video!!! :) However, all I have are the videos - no book or articles.

[@biancamanago3214]

This is an excellent resource. Thank you!

[@statquest]

Thanks! :)

[@Dr.HusseinEid]

Hi josh i am from somalia your videos helped me to understand logist regressions , your explanation is very good thank you😊

[@statquest]

Thank you! :)

[@mrstudent1957]

i recommend your channel whenever people ask me where did i study from

[@statquest]

Thank you very much! Sharing my videos is the best complement. :)

[@shnokoiek3528]

You are absolutely an amazing stat teacher :)

[@statquest]

Thank you very much! :)

[@vinodaxisful]

Hi. I am trying hard to find out the calculation for arriving at the standard error of the co-efficient and the intercept. Would be helpful if this can be shared.

[@brainfuck007]

Data Science is nothing without Statquest

[@statquest]

BAM! :)

[@jiayiwu4101]

In summary, there are five graphs/function within logistic regression. 1. p-odds: y = odds = p/(1-p). this is a part of inverse function p belongs to [0,1] and odds belongs to [0,inf). Two parts are p1/2 2. odds-log(odds): y = log(odds) this is a normal log function where odds belongs to [0,inf) and log(odds) belongs to (-inf,+inf). Corresponding two parts are 0

[@statquest]

Bam!

[@AnahideCastro]

It´s just amazing! Thank you very much! It´s funny and accurate. Your classes are inspiring.

[@statquest]

Thank you! 😃

[@leavonfletcher4197]

Greetings from the University of Texas at Austin! I am going through a Machine Learning class and your classes are totes useful! Thanks!

[@statquest]

Totes Bam!

[@rrrprogram8667]

One request... All the videos available are randomly watched.... But can you suggest the sequence to watch.. So that the content becomes more structured for the learning path of ML

[@wizeguy9285]

You can go to the playlists option on the home page and watch them in order by topic

[@XYZmmc]

@@wizeguy9285 but there will not be correct order

[@TheIsrraaa]

OMG find a full path on Internet for ML. Statquest is one of the best channels on KZbin but ML its much more than just a playlist to follow.

[@thulasirao9139]

Go to play list you can see in order. You need to subscribe for that

[@markparee99]

Well done! Very well explained.

[@badoiuecristian]

This litterally could not have been any clearer. I have now 0 questions about this topic. Amazing teaching skills.

[@statquest]

Hooray!!!! Thank you very much. :)

[@badoiuecristian]

@@statquest Pam Pam!

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The best explanation ever. Thank you Sir.

[@statquest]

bam! :)

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discover this channel is the best thing happened to me!!! GRACIAS!!!!

[@statquest]

Bam!

[@pranaymehta7958]

Hey Josh, thanks for the simple and clear explanation about Logistic Regression. I have a question about this technique - where and how do we include the hyper parameter terms for the Logistic model ? Also, what are the implications of various hyper parameters when we add it to the loss terms? I think it would be really nice if you can explain the Lasso and Ridge techniques with this intuition of Logistic Regression. Thanks :)

[@sallywang9894]

thank you so much for making this series of vidio! helps a loooot

[@statquest]

Thanks! :)

[@RCConsultant]

Thank u so much for helping me in my journey of data .

[@statquest]

Good luck! :)

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I think your channel is awesome! Thanks for doing this!

[@statquest]

BAM! :)

[@user-mn8th3ie1t]

A very informative video. A slight observation re.terminology. In any regression modelling, Let’s take your example of predicting size of a mouse using weight as a predictor, what you’re actually predicting is not the size of a mouse, but the expected size of a mouse given its weight E[size /weight] = intercept + b0*weight. It’s crucial to introduce that probabilistic reasoning at an early stage. The idea that we’re trying to predict the expected value of the target variable given the value of a predictor, independent variable, betrays the method that we want to find the regression coefficient of weight that would render observing the size most likely, hence the famous MLE - Maximum Likelihood Estimation.

[@gsp_ram]

❤ this channel. Completed my understanding...

[@statquest]

Awesome, thank you!

[@katharinastck]

I love the way you explain complex concepts in such a simple and understandable way! I'm currently doing a professional training in machine learning and many things that are just brought to me by complex equations are so much easier to grasp with your videos! If I could wish for something, it would be some additional Python videos. You do a lot with R, but I feel like Python is requested more often in the non-academic world.

[@statquest]

Thanks! I'm starting to add more python videos.

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Thanks for this rich content, best educational video about machine learning, youre the best!!!

[@statquest]

:)

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Brilliantly articulated

[@statquest]

Thank you! :)

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omg...your songs are awesome. i just visited your website and listening full songs.its awesome.So many Bamsss

[@statquest]

Thanks so much!!! I'm really glad to hear you like the songs. :)

[@rrrprogram8667]

I will watch this many times till it sinks in my head

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Thank you. This is very helpful.

[@statquest]

Thanks! :)

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I all the time watching the videos of StatQuest and just wondering for two things: 1) Why there is no actual course, after which you can get a certificate as the teaching methods, explanation and instructor are awesome? 2) There are few, but still there are some people who click on 'dislike' sign to the video. I was wondering why, as there is no doubt that the instructor is explaining like for kids. For example, I have checked the PCA model for data reduction and StatQuest's explanation was the only one from which I finally got the idea of what is going on. So, BIG thanks to StatQuest...

[@statquest]

Thank you very much! I would love to make an actual course - and maybe one day I will. Right now I'm spending all of my time making videos - that's my favorite part, so that's what I do. :)

[@Niceperson7428]

@@statquest while no course, will follow your videos :)

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Statquest =infinite positivity

[@statquest]

BAM! :)

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Thanks Josh. I’m hooked. MS Data Analytics & Viz. in view 🙏🏿

[@statquest]

bam! :)

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I can safely say that StatQuest is super-logit!

[@statquest]

ha!

[@m.umutcanoluk3163]

Hi, I want to apply logistic regression to a dataset that consists of accuracy scores taken out from 3 different groups, but I don't know how to enter that to the analysis. What I mean is, what becomes predictor, and what becomes outcome in a group of 3? How do you analyze that? Could you by any chance give me an idea on that? Thanks!

[@krzysztofkolmus6936]

That was another great video! Thank you so much!!! Just a quick question, have you published any book on statistics, machine learning, programming, etc? I'd love to have it!

[@statquest]

Unfortunately, these videos are all I have. Maybe one day I'll put them all together into a book.

[@scoppyeah]

Best explanation 👍

[@rhlongwane6575]

Best logistic regression tutorial.

[@statquest]

Thanks so much!!! I'm really happy to hear you like this one. I was worried it would be too obscure.

[@rhlongwane6575]

StatQuest with Josh Starmer It is not obscure at all; just perfect.

[@statquest]

Thank you! :)

[@eamonnca1]

Our prof speaks broken English and does not explain this stuff very well. You are a life-saver!

[@statquest]

Thanks!

[@drachenschlachter6946]

Triple Bam!! Good video!!!! Greets from. Germany 🇩🇪😍

[@statquest]

Danke! :)

[@ethiopiantech]

3:08 I can't stop laughing at your hilarious voice tone when you say "shameless self-promotion"! It's cracking me up!

[@statquest]

Bam! :)

[@baraalrefai1238]

Thanks, Man you help me a lot.

[@statquest]

Hooray! :)

[@TheRobsterpunch]

Wow what an awesome video! Thank you so much! Just one more question: You talk about the interpretation of the weight = 0 leading to a log(odds of ob.) of -3.476 (minute 9:00) and I totally got that. But what about the case when there is more than one predictor in the formular? Is it still possible to interpret the intercept?

[@statquest]

Great question! When you have more predictors, then the intercept is the log(odds) when all of those other predictors are 0. Does that make sense?

[@TheRobsterpunch]

@@statquest Yeah it does, thanks for the quick answer!

[@yzadil]

Statistics with fun! I like it a lot. Thanks.

[@statquest]

Glad you enjoyed it!

[@soumyasharma5743]

Hi Josh, thank you so much for this fantastic video! I was wondering if there are more study guides on the way? Not just for this topic but for others too e.g. R squared / Log odds etc. They are so awesome, I would be inclined to buy them!

[@statquest]

I'm almost done writing The StatQuest Illustrated Guide to Machine Learning that covers all kinds of stuff. It should be available in early 2022. BAM! :)

[@kavuruvamsikrishna02]

excellent Josh

[@statquest]

Thank you! :)

[@sheilaquan9824]

One of my fav sources of education now! ( this song .......)

[@statquest]

Thanks! :)

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Hey Josh, awesome stuff.Landed on your channel after 3b1b ....Quadruple BAM !!!

[@statquest]

Hooray!!! I'm glad you like my stuff! :)

[@junayedhasan]

Professor Josh, I have a question. The best fitting candidate line we draw here, but on x axis how to determine where to intersect ? I mean how will I draw the best fitting candidate line ?

[@kakusniper]

Always pleasure to understand statistical concepts, I was wondering if you have any recommendations for any books to learn statistical modelling (related to genomics) ?

[@statquest]

Glad you enjoy the video! Unfortunately, I don't have any good book recommendations. I've enjoyed the free "Introduction to Statistical Learning", but that's not really what you're after.

[@philocalist_leon]

Great video !

[@statquest]

Thanks!

[@a.tanveer9663]

Fantastic explanation, as always. For anyone looking for a deeper-diver into the math, chapter 4 from 'An introduction to Statistical Learning' is highly recommended.

[@statquest]

Bam!

[@MrPainfulTruth]

The critical part is the link between a normal variable, the probability and the log odds results. You explained a bit of it and i didnt see any better video, but i'd lie if i said i understsand that step already to a degree that i could explain it to someone myself.

[@statquest]

For more details on that step, see: kzbin.info/www/bejne/eJeukqGiZsaGfZI

[@thirdanonymousacc]

Thank you so very much!

[@statquest]

:)

[@distancelearningtelelangue8794]

I grew a little lost when the samples of mice where moved to the - y and -x lines althought it is explained...I suppose I shall review the t-test to better understand?

[@ratnakarbachu2954]

love u brother , god bless u. u r rock.

[@statquest]

Thanks!

[@eajaykumar]

OMG Josh, after watching your videos one by one that is Logs ,Odds and Log(Odds). Logistic Regression is just tip of iceberg Double BAMMM!. ( StatQuest - youtube infinity = StatQuest Infinity)

[@statquest]

Hooray!! BAM! :)

[@rrrprogram8667]

Hit like and watch... Loving it

[@antygona-iq8ew]

Great video.

[@statquest]

Thanks!

[@zukofire6424]

Thanks Professor Josh Harmer (I have a presentation tmrw!!) sending gratitude and good vibes!

[@statquest]

Best of luck!

[@zukofire6424]

@@statquest I passed! ^^

[@statquest]

@@zukofire6424 TRIPLE BAM!!! Congratulations :)