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Statistics 101: Linear Regression, Fit and Coefficient of Determination 

Brandon Foltz
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This Statistics 101 video is the next in our series about Simple Linear Regression. In our last three videos, we talked about the very basics of regression and introduced other fundamental concepts like the algebra of lines, general patterns to look for on a scatter plot, and the least-squares method.
In this video, we are going to learn to evaluate how well a regression line fits the data it models. It is important to note that a regression model is unique to the data it represents. Adding or changing data points will most certainly change the regression model. The model is also only valid for the range of data points under analysis. It is not proper to extrapolate above or below the data being evaluated.
So if you are new to Regression or are still trying to figure out exactly what it even IS...this video is for you. So sit back, relax, and let's go ahead and get to work.
My playlist table of contents, Video Companion Guide PDF documents, and file downloads can be found on my website: www.bcfoltz.com
#statistics #regression #machinelearning

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7 авг 2024

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Комментарии : 526   
@antoniogiuseppefaietalasar6849
@antoniogiuseppefaietalasar6849 3 месяца назад
This is the gold standard for statistic teaching. Indispensable.
@Yu-Xiao-2028
@Yu-Xiao-2028 3 года назад
I don't skip your intro because I needed that positivity in my life right now
@rohitekka2674
@rohitekka2674 3 года назад
More than 7 years later, and your videos still continue to bring wonders. Thank you!
@wbspangie
@wbspangie 8 лет назад
Stared at the book for hours yesterday and understood nothing. Watched this videos and 20 minutes later it all makes sense! Your are amazing! Thank you!
@MegaApostolicMan
@MegaApostolicMan 8 лет назад
I had the same experience. Looking at the book, and the Professor video. I just could not make sense of it, until I see these videos.
@pushkarmahajan9294
@pushkarmahajan9294 2 года назад
SAMEEEEEEEEE ;_;
@RoboticComplexity
@RoboticComplexity 4 года назад
I used to get so frustrated I would cry trying to read my textbook. I passed Linear Regression I with a B because I watched your videos. Now on to LR II and I'm refreshing my memory. Thanks.
@jackeroo75
@jackeroo75 3 года назад
Keep it up and be positive in yourself and you will get better and better!
@ireneborgen8035
@ireneborgen8035 4 года назад
I finally understood what SSE and SSR are... and what "fit the data" is... amazing!
@annatsukiya
@annatsukiya 8 лет назад
now i know what's the use of SSE, SST and SSR.. during my studies, lecturers just tells us to memorize it without explain the why we use those in steps of making regression table.. Thanks Brandon, i'm looking forward to learn Multiple Regression next..
@tubeymoto
@tubeymoto 6 лет назад
same here.... hahaha
@shela3081
@shela3081 3 года назад
same !
@Pankajkumar-dw1fu
@Pankajkumar-dw1fu 5 лет назад
I always like the motivation you give at the start of every lecture.
@gatr12isthebest
@gatr12isthebest 7 лет назад
I got more knowledge in intervals of 20 mins with you, than in a university level class of 1hour of which I have to pay for. Says a lot about my country's education system. Great job.
@sunra7712
@sunra7712 7 лет назад
best teacher since Sal Khan
@BrandonFoltz
@BrandonFoltz 7 лет назад
Very kind of you to say. Sal is a HUGE hero of mine bringing education to everyone.
@Qornv
@Qornv 4 года назад
@@BrandonFoltz While Sal is doing an incredible job, and has helped me as well several times, in my opinion you explain topics better, maybe because you're focusing on mainly statistics while Sal tries to cover as much as possible
@juliusbenkoe5373
@juliusbenkoe5373 3 года назад
Imho on par with Sal. Thanks a lot for lifting the fog!!!
@courtneywilkerson6131
@courtneywilkerson6131 3 года назад
This channel the best in my opinion.
@juliusbenkoe5373
@juliusbenkoe5373 3 года назад
@@courtneywilkerson6131 that's absolutely true!
@LRZ2628
@LRZ2628 2 года назад
Thank you so much for this! After 7 years away from Master's-level statistics, I'm earning my PhD and totally stuck on the path of regression, exploratory and confirmatory factor analysis. Your videos are an absolute life-saver!
@samanthadunley
@samanthadunley 3 года назад
I've learned more in this 30 minutes video than my 2 hour lecture at school!!! I really appreciate the time and effort you put into these videos! Thank you so so so so so much!
@shivakumarkeshavan5171
@shivakumarkeshavan5171 5 лет назад
Brandon - I have gone through a few videos of regression and I love the way you have simplified things + a beautiful pattern of beginning with a wonderful quote, pictorial representation and ending by wishing everyone the best - Thank you!
@Elethia441
@Elethia441 8 лет назад
OMG, my textbook writers must be sadists! This makes so much more sense!
@dijonstreak
@dijonstreak 4 года назад
Man no kidding
@ol7668
@ol7668 5 лет назад
Such a great lecture series that I've ever had on RU-vid. Watching all ads for my tuition.
@JoshFlorii
@JoshFlorii 7 лет назад
Amazing series. 8 years after going over this in highschool I finally understand it.
@omarflores527
@omarflores527 8 лет назад
Hi Brandon, You are doing an awesome job man. Thanks for taking it slow on these concepts and providing a well thought out presentation with applicable examples. Trying to pass research comp exams for my Ph.D. in education and this is incredibly helpful! Thanks again, keep up the great work...
@goldiekaur928
@goldiekaur928 9 лет назад
hey Brandon. thanks a lot for posting such brilliant videos..I salute you for teaching in such depth and clarity that too free of cost..people like you make this world a better living place.
@naageshk1256
@naageshk1256 9 месяцев назад
Agreed :)
@fwlanger
@fwlanger 8 лет назад
Brilliant videos! I've just finished watching all your linear regression lessions, and I can certainly tell you are making my Biostats studies much easier and pleasant! Huge thanks from Brazil!
@markzhang8742
@markzhang8742 10 лет назад
Best regression class I have ever had!
@renewmasonry8176
@renewmasonry8176 7 лет назад
brandon, At 56 years old, I have decided to return to school...I'm taking elementary statistics, starting on 30 days, but have been pre studying to get a jump on things. I haven't done any math in 30 years. I enjoy your teaching style, and what shines through is that you truly care. You're a great coach!!
@BaldwinThamaga
@BaldwinThamaga 10 лет назад
It's not often that one can scroll down a list of comments on RU-vid without bumping into a single negative one. Goes to show how helpful your videos Brandon. Thank you.
@edwardmoor6538
@edwardmoor6538 9 лет назад
Your a great teacher. Made regression so much easier for me. I really appreciate the time you took to upload these!
@PrachiR
@PrachiR 8 лет назад
thank you so much! you are doing a great job!! - you explain so well.
@PinkFloydTheDarkSide
@PinkFloydTheDarkSide 7 лет назад
I paid $5k for stats class in my program and studying it for a year and today by this video I understood what R square actually means and how does it explain the variance. Thank you from the core of my heart.
@MuhammadAli-yq7sd
@MuhammadAli-yq7sd 10 месяцев назад
After nine years, your videos are much valuable than ever. Who knows who knows who will take advantage of them after another years. You can't imagine how young I was.
@sabinagargosova1951
@sabinagargosova1951 3 месяца назад
You just saved one desperate Psychology student, thank you.
@fridaysilomba8444
@fridaysilomba8444 4 года назад
I have done this from my undergraduate, I started it in my First Stage at Masters and Never knew what really goes on until after Watching your videos from The basics.. I wish you could see how Fast I answered The Class Tutorial Question.. Thanks and Many Thanks.. You are simply the Best
@ilikedetectives
@ilikedetectives 6 лет назад
Thank you so much Brandon. I'm taking a grad-level stat course without any basic stat knowledge and your videos have been life-savers!
@sandeepdesai5378
@sandeepdesai5378 3 года назад
Best explanation of what SSE, SST and SSR mean anywhere on Internet!! Thank you. You have a gift of an awakener!
@BrandonFoltz
@BrandonFoltz 3 года назад
Glad it was helpful! If you get those down, all of regression opens up. Keep at it!
@redserpent
@redserpent 5 лет назад
Amazing series. I had tried for several years to understand and fit together both the notation and the concept. Well done and thank you. Clearly a share URL.
@donharris8846
@donharris8846 Год назад
This video should be required for ALL basic stats courses. From elementary to grad school this is, hands down, the best explanation to help people gain an intuitive sense of what a regression truly is. Very well done.
@davidgl1988peru
@davidgl1988peru 4 года назад
You are INCREDIBLE Brandon Foltz. Thank you so much!
@sketchstudios05
@sketchstudios05 8 лет назад
"Thank you " word is not enough to express how much thankful I am to you. BIG THANKS, your video explain LR in very simple way.
@eternity3061
@eternity3061 7 лет назад
The fourth and the last video, and I know the basics of linear regression. The best part is that even if I watch the videos over 4-5 days, I don't feel any disconnect. The short review/references to the previous videos are really helpful. Thanks Brandon for all the hard work.
@abundant_AF
@abundant_AF 3 года назад
You are a fabulous teacher! Wow. I am so impressed with your patience, your positivity and your clarity in explaining these concepts. I am taking stats this term and these videos have been an invaluable supplement to my course materials. I am so grateful to you! Thank you for everything.
@emilyconley4967
@emilyconley4967 8 лет назад
Another exemplary video. Thanks, Mr. Foltz, you are a wonderful teacher!
@mks07866
@mks07866 8 лет назад
This is one of the best training videos I have ever seen. I am taking a applied analytics frameworks course at Columbia University and this course really helped me to understand the concepts before I jump into more advanced topics. Brandon, can't thank you enough!!
@darcimartindale4861
@darcimartindale4861 8 лет назад
You're actually saving my life! Thank you so much for explaining in one video what my prof couldn't do in 3 weeks!
@eszterarato1490
@eszterarato1490 8 лет назад
All Simple Linear Regression videos are excellent learning materials. It feels so great to be confident about this topic, finally. I am really grateful.
@ozlevy4057
@ozlevy4057 7 лет назад
Thank you Brandon ! very straight forward and clear. Please keep on making these videos to help those who need it.
@cccspwn
@cccspwn 4 года назад
Phenomenal, a good teacher is worth his or her weight in gold, you are worth your weight in platinum!
@santoshpandey23
@santoshpandey23 9 лет назад
I actually clapped at the end the 4th video...Thanks a lot Brandon Foltz..going back to basic was so exciting...
@biswashgauchan5644
@biswashgauchan5644 10 лет назад
Brandon, the video is just too good. I have benefited a lot in understanding the basics of regression. Excellent work and great service to education
@rtong12
@rtong12 10 лет назад
You are a very gifted teacher. Love the slides that you built. I've heard this topic explained so many times and I think this is the first time I truly understand how R square is calculated. Thank you!
@ilhamhamza10
@ilhamhamza10 9 лет назад
Without a doubt the best presentation I have ever seen on Linear Regression! This video sums up the whole theory behind the topic and completely puts my professors to shame!! Well done Good Sir!
@sumanthgoje6864
@sumanthgoje6864 5 лет назад
Brandon ...you deserve standing ovation ...thanks much ...
@bruschetta3089
@bruschetta3089 6 лет назад
And five years later you are still the person who explain the best!!
@maryhabashy8663
@maryhabashy8663 4 года назад
FABULOUS!!! This was a great visual representation of Simple Linear Regression! As a visual learner, this made this concepts much more approachable. Thank you Brandon.
@sarojsasmal
@sarojsasmal 5 лет назад
I love your presentation, the way you begin your tutotial, especially the first few lines in the very beginnning really keeps me motivated. Thanks a lot.
@mohammedalswailem3868
@mohammedalswailem3868 7 лет назад
Thank you for sharing your knowledge with the world. You are making the world a better place with each video you make and each view you receive. I had a rough time catching up to the lectures and you made it easy. I wish I have found your channel earlier in the semester not two days before the final. Thank you again
@varunbhargava15
@varunbhargava15 7 лет назад
The best tutor I have came so far for statistics, you make things look so simple to understand. Thanks a ton for simplifying the things for us.
@zoebeary
@zoebeary 10 лет назад
Can't thank you enough! Having to challenge an old stats course exam in preparation for my Master's! Your approach and genuine love for teaching is getting me through!!!! Fingers crossed!
@sienna367
@sienna367 6 лет назад
Thank you!!!!!!!! I'm a fresher in data science! And your videos are *MAGIC*!!!!!!! I've finally understood a lot of topics in regression... thank u!!!
@25lobo
@25lobo 9 лет назад
This serie of tutorials is the best thing I have ever seen about linear regression! Show!
@gustavomello278
@gustavomello278 6 лет назад
May god or whatever you believe the most bless you. I cannot express how much grateful I am for all your videos. Positive message meets amazing teaching.
@tracygundy4038
@tracygundy4038 9 лет назад
Thank you really much Brandon! I am an international student doing a master program and this videos are very useful for me. You make difficult concepts easy to understand (even for a native-spanish speaker with a not so advanced English), and that's what makes a teacher outstanding. Thanks.
@manjuk8363
@manjuk8363 6 лет назад
These are the ideal set of videos for even a layman to understand stat in and out! Thank you very much for the videos
@nozepark5555
@nozepark5555 2 года назад
8 years later and still this video saves the day!
@jinghua7561
@jinghua7561 4 года назад
It is the best online course I have ever watched. Thank you!
@jelenamiokovic5658
@jelenamiokovic5658 7 лет назад
I have never seen a better teacher in my life!! you are AMAZING!!! keep it up!
@iidamakikallio8599
@iidamakikallio8599 7 лет назад
You sir are eliminating so much stress from the planet. You deserve a public health honor of somesort. Thank you SO MUCH. Absolutely fantastic pedagogical skills. You rock. Biggest of thanks.
@thaddaeuscarr9886
@thaddaeuscarr9886 4 года назад
These lessons will always be relevant! Thank you for these breakdowns!
@ritchiebrowne4629
@ritchiebrowne4629 3 года назад
This is brilliant Brandon, just watched all videos on Linear Regression and you explained more in 2 hours than my college lecturer did over 3 weeks
@petragonzalez7868
@petragonzalez7868 2 года назад
You're a super start. I feel frustrated because after watching your videos I feel I have been fooled at school. How much simpler would have all been should we have been explained in such terms? It is mind blowing.
@akankshat3395
@akankshat3395 5 лет назад
I liked and subscribed immediately when it said "ITS A TALE OF TWO LINES"!! Great Explaination
@misnadin6658
@misnadin6658 10 лет назад
Thank you so much, Brandon! This is an excellent explanation of what linear regression is!
@taraplachowski9774
@taraplachowski9774 6 лет назад
This truly makes linear regression logical and understandable, rather than memorizing steps in SPSS. I now understand interpretation of social science statistics in a way I have not after 4 stats classes in my doctoral degree. Thank you! I will be sharing these videos with all my fellow doc students! Looking forward to MR!
@ranjithpals
@ranjithpals 4 года назад
Great job Brandon! You are the best I have come across explaining the math behind the algorithm.
@millazilla3811
@millazilla3811 7 лет назад
you rock!!! I wish all online stats classes were like this. I hope you continue making videos you stats wizard!!
@sunkyongkim2886
@sunkyongkim2886 4 года назад
I cannot even find proper words to express my gratefulness to thank you sir. Thank you for the clear explanation. It feels like you throw a rope for me to escape from a lonely and dark underworld hole of statistics.
@leannewong6296
@leannewong6296 7 лет назад
After watching all your videos on simple regression , i am definitely more comfortable with the concepts now and can start working on quantitative methodology for my thesis. Thanks so much! You've done a great job at breaking things down such that it's so easy to follow. Subscribed :)
@fysiologieee
@fysiologieee 8 лет назад
we need more people like you that do these good things for free ;)
@jazaysurfclub2568
@jazaysurfclub2568 8 лет назад
Brandon, all the students in artificial intelligence must do you a tribute, you are the king dude ! thanks ! ..i highly recommande all the fox, to see the videos of linear regression before doing a step in machine learning. Thanks King Brandon.
@vidyanarayanan3872
@vidyanarayanan3872 6 лет назад
at age of 40, i am trying to understand stats to become a data scientist. These videos are assuring me that i will be able to understand stats easily. thanks a ton brandon!
@suahantkulkarni2350
@suahantkulkarni2350 6 лет назад
Thanks Brandon, Iam just getting amazing basic knowledge about simple linear regression. Looking forward for all available tutorials from you. Thank you very much
@ashfaaqasif8010
@ashfaaqasif8010 9 лет назад
You're a life saver my friend! Thanks!!
@empaulstube6947
@empaulstube6947 4 года назад
Thank you Sir Brandon!!! I have encountered this Regression topic many times in my teaching and studying career. But this is the only time I learned.
@JohnsonHinneh
@JohnsonHinneh 9 лет назад
sure this video is so good, it has enlightened me so greatly on how simple regression works. I am now confident in digging deep into statistics.
@Miamiheat434
@Miamiheat434 9 лет назад
I am passing my Intro to Stat Analysis class b/c of you and your terrific videos...thank you from the bottom of my heart.. I look forward to seeing your Multiple Linear Regression ones..
@arturoolvera2604
@arturoolvera2604 10 лет назад
WOW! I was amazed to finally understand why we use linear regression! Thank you!
@mirimar69
@mirimar69 9 лет назад
Thanking you for all your effort Brandon. Clear and succinct presentations. As a mature learner I was putting off this seemingly dry topic but no more! I will continue persevering Thank you and season greetings from down under.
@BrandonFoltz
@BrandonFoltz 9 лет назад
mirimar69 Awesome! Thanks for very nice comment and I am glad you found the fire to learn what definitely can be a dry topic. Season's Greetings to you as well from the cold North!
@rawa9891
@rawa9891 5 лет назад
Very, Very GOOD. Nice and calm and to the point. Now I've got it because you did a VERY good job. Thank you !
@vivayk
@vivayk 7 лет назад
u made me understand regression in 90 mins..awesome work!! and thanks a bunch
@IsisMarques
@IsisMarques 6 лет назад
Thanks so much for the videos, it's really well-explained and helpful! I really learn much more when the teacher uses the same exemple all along the process, like a simple case study. Thanks again!
@sharifahmed45
@sharifahmed45 4 года назад
Thanks Dr Foltz, this playlist helped immensely my understanding these ss's that confounded me. I will restart stat101 to deepen my understanding. Thanks again, and continue being productive to help struggling student anywhere in the world.
@KirillBezzubkine
@KirillBezzubkine 4 года назад
With every new video i watch i worship your tut abilities and effort
@frederickfinau3628
@frederickfinau3628 6 лет назад
Amazing! You're brilliant and you have made statistics more enjoyable for me personally. Your videos give lots of clarification for basic statistical concepts for my further study. Keep it up your good work and am following your posts from now on. Looking forward for more ......
@amitkumar5579
@amitkumar5579 2 года назад
Thank you again !! for such an amazing video to let us understand complicated things in a easy way.
@stevenws413
@stevenws413 9 лет назад
I have always struggled with the concept of squaring values in a regression model but your method of visualizing them as... well... squares, turned the light bulb on for me! Thanks!
@roshanwickremasinghe7555
@roshanwickremasinghe7555 3 года назад
Thank you very much for your videos. Simple, Clear and to the point. Helped me a lot in my assignments.
@peterm9001
@peterm9001 8 лет назад
in the last graph you put the estimation of y instead of the mean equals 10. Thank you so much for your work it helps a lot!!
@kevinha3192
@kevinha3192 4 года назад
Thanks man !!! This is great ! I have never taken statistic before , I have to do deal with data relate to linear regression , this totally clears it up !!!!!!
@adelemurphy7681
@adelemurphy7681 9 лет назад
Great videos, I'm so grateful I found you after painfully trawling through books and lecture notes. Finally a clear explanation. Actually don't feel overwhelmed by my stats class tomorrow :)
@molan011
@molan011 5 лет назад
Listening this videos to remind myself of some things learned many years ago...very useful also for us developing models for phd thesis...good job sir
@NandkishoreKulkarni
@NandkishoreKulkarni 6 лет назад
Thanks a lot for the videos.. really helped to understand from the scratch. I was zero before watching, now I can confidently say I have learned a bit.. thanks again.
@joshyujimeek
@joshyujimeek 10 лет назад
Very, very helpful! Look forward to many more of your videos.
@Xeena81
@Xeena81 8 лет назад
Amazing work and effort, very clear and straight-forward... I never understood regression this way before...THANK YOU :)
@sarehpanjeh724
@sarehpanjeh724 5 лет назад
Thank you, Brandon Foltz. You are the best teacher I 've ever seen.
@AKumar-gj5zv
@AKumar-gj5zv 7 лет назад
Thanks for the Great knowledge sharing efforts ! It has been helping us a lot. I appreciate your spirit, Brandon !!!!!
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