Linear Regression, Clearly Explained!!!

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  • Опубліковано 23 гру 2024

КОМЕНТАРІ • 278

  • @statquest
    @statquest  2 роки тому +26

    NOTE: 25:39 I should have (Pfit - Pmean) instead of the other way around.
    Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/

  • @tonysvlogs881
    @tonysvlogs881 Рік тому +64

    I struggled understanding this topic through a textbook/ professor videos online, and this was just a great explanation. It was like watching this video, made all the pieces finally fit

    • @statquest
      @statquest  Рік тому +3

      Hooray! :)

    • @Bang-_-Bang
      @Bang-_-Bang 11 місяців тому

      Yo bruh seriously I don't understand anything 😭😞

    • @ricardorodrigues4726
      @ricardorodrigues4726 2 місяці тому +1

      The trick to read hard books is to completely ignore the over detailed math explanation on a topic you don't understand. Why? Because Math needs to be thorough and in doing so it over complicates. I can't tell you how many times when I was starting, I was struggling to understand an algorithm because I was reading the math of it and then I would ask for help from a teacher or collegue, which would explain to me in ENGLISH, what the algorithm did, then it become obvious and the math too afterwards. In any Computer Science field that shows proofs or uses math to explain concepts, completely ignore it, learn the concept first, the math will follow.

  • @NamNguyễnHoài-f2s
    @NamNguyễnHoài-f2s Рік тому +26

    I'm an electrical engineer who wanted to learn about machine learning, and your videos helped me understand all the fundamentals of this field. Thank you so much, sir

  • @infamousprince88
    @infamousprince88 Рік тому +34

    This assisted me in delivering a presentation for a job interview -- landed the opportunity.
    Thanks!

    • @statquest
      @statquest  Рік тому +14

      TRIPLE BAM!!! Congratulations!!! :)

  • @fooballers7883
    @fooballers7883 9 місяців тому +14

    I wish I had your lecture 50 yrs ago.... never too late learning it again today. thank you

  • @imakechannel
    @imakechannel Рік тому +13

    I struggle understanding this topic but it is Great to learn from someone who can explain things in a simple manner with eloquence

    • @statquest
      @statquest  Рік тому +1

      Thanks!

    • @a.qais6697
      @a.qais6697 Рік тому +3

      @@statquest Agreed. You articulate well and make the subject simple and easy to understand.

  • @undeadsatan3317
    @undeadsatan3317 Рік тому +88

    I'm in my stats class but watching this instead of listening to my professor lol 💀

  • @kimiko495
    @kimiko495 9 місяців тому +2

    wow this make so much sense! I'm pissed why college professors don't teach like this, it was a waste of time to sit in their classes being so confused right from the start. I can't thank you enough for your videos!

  • @ioanamihai4368
    @ioanamihai4368 2 роки тому +8

    Wow...i was searching for this on your channel last week and I was so sad I didnt find it... luckily i still have time to study for the test. Thank you!

  • @Épicesdelien
    @Épicesdelien 10 місяців тому +2

    Love the musical introduction. Such a nice touch to prime you beforehand :)

  • @DSharma117
    @DSharma117 7 місяців тому +2

    Thanks Josh, your channel is recommended from Murdoch University,Australia lecturers. Worth watching your channel

  • @AbhiSarangan
    @AbhiSarangan 6 місяців тому +2

    I would be lost without this channel

  • @NaderNabilart
    @NaderNabilart 2 роки тому +5

    Great work! The graphics made it super easy to understand.

  • @user-bz7fj1fk2m
    @user-bz7fj1fk2m Рік тому +3

    10QUVM for your valuable presentation!!! You made me feel proud in my STAT!!!

  • @jenwilson7779
    @jenwilson7779 Рік тому +1

    Thanks!

    • @statquest
      @statquest  Рік тому

      BAM!!! Thank you so much for supporting StatQuest!!!

    • @jenwilson7779
      @jenwilson7779 Рік тому +2

      Of course! I am the person who is embarrassed on the inside that I don't get the stats terms when thrown around at work, but know that I'm memorized them so know what they are, but really don't understand the "why" or how it all relates. Thank you so much for speaking slowly in your videos, reiterating concepts, sometimes with additional concepts in between, and your humor. It's fun. I'm grateful. @@statquest

  • @fabslyrics
    @fabslyrics 9 місяців тому +2

    thank you friendly folks of the genetics departement of NC Chapel Hill , greetings from Paris France.

  • @anlinli6463
    @anlinli6463 Рік тому +4

    Thank you Josh! You are truly helping me with the difficult reviewers' comments🤣.

  • @jamesahn3865
    @jamesahn3865 2 роки тому +2

    I had to buy a study guide book after watching this video...! This is a great video!!

    • @statquest
      @statquest  2 роки тому

      Thank you so much for your support!

  • @antonyshadowbanned
    @antonyshadowbanned 2 роки тому +2

    You are indeed a God among mortals. And as such you shall be praised. Tons of gratitude for blessing us with your pristine insight Father Majesty.

  • @minhvule1608
    @minhvule1608 Місяць тому +1

    Never forget to hit a like to the videos of this channel. It's totally worth it.

  • @montasiraffan-cu7xk
    @montasiraffan-cu7xk 2 місяці тому +1

    literally top notch i have ever seen.
    thanks man

  • @bhargav1811
    @bhargav1811 2 роки тому +3

    This was truly advanced concept for me !!! :)

  • @penguinmonk7661
    @penguinmonk7661 Рік тому +1

    I always have a good time with Statquest :3

  • @mahammadodj
    @mahammadodj Рік тому +2

    Does n equals to the number of data points in F equation? For example, we should take 9 for n in 22:40 ?

  • @lmina3425
    @lmina3425 29 днів тому +2

    this is just brilliant work!! thank you very much and pls continue teaching :)

  • @SofiaBuyanova
    @SofiaBuyanova 2 роки тому +4

    Thank you for the great video! Please note that from the second 25:49 the degrees of freedom for the numerator should be (Pfit-Pmean), otherwise it is less than 0.

    • @statquest
      @statquest  2 роки тому +1

      Thanks! In theory UA-cam is supposed to alert people of that typo, but maybe it doesn't always work. (I just tried it and it worked for me).

  • @lizs7827
    @lizs7827 6 місяців тому +1

    Awesome video, thank you Prof. Josh!!!!!

  • @missthuli2340
    @missthuli2340 5 місяців тому +1

    Thank God i came accross your videos. Making my CFA journey towards statistics less overwhelming by explaining like you are explaining to a 5 year old...pheeewww.

  • @12PEN12
    @12PEN12 Рік тому +1

    Hats off to StatQuest!!!

  • @muhammedfarispk1687
    @muhammedfarispk1687 Рік тому +1

    I am enjoying this teaching method 😍

  • @rahoolmahool-programming5499
    @rahoolmahool-programming5499 Рік тому +1

    I got pregnant two times while learning SGD from you. This is the hundredth time i'm jumping from a video to another video.

  • @kuraldeepdives9319
    @kuraldeepdives9319 Рік тому

    @26:21 Should the curves say ( P fit- P mean)=1 ?

    • @statquest
      @statquest  Рік тому +1

      Yes! That's funny that it's been like that forever, but you finally caught it. Thanks!

    • @kuraldeepdives9319
      @kuraldeepdives9319 Рік тому +1

      @@statquest Haha the credit goes to you for teaching the concepts so well to a newbie! BAM! 😁

  • @timbui5556
    @timbui5556 Рік тому +1

    Thank you for making this series of statistic videos. One question please: I want to calculate the least squares growth rate of sales for a company. Would I have "higher quality" growth rate by using quarterly sales (40 pieces of data) vs. annual sales (10 pieces of data). Would the seasonality (Christmas sales higher) affects of quarterly sales and distort the growth rate? Thanks,

    • @statquest
      @statquest  Рік тому +1

      It sort of depends on how exactly you want to model and what you want to get out of the model. If you want to take seasonality into account, then you need to fit a periodic function (like a sine function) to your quarterly data. That said, the easiest thing to do would be to start with annual sales and see how useful that is.

    • @timbui5556
      @timbui5556 Рік тому +1

      @@statquest Thank you so much for taking the time to answer my question!

  • @derekc.5063
    @derekc.5063 6 місяців тому

    At 15:15, how does least squares cause any useless variable to be multiplied by 0? I thought Lasso regression excludes variables.

    • @statquest
      @statquest  6 місяців тому

      Least squares can do it in principle, but not very well. Lasso is much more effective, and lasso also works when there are more variables than data.

  • @marm_sam_bamb
    @marm_sam_bamb 9 місяців тому +1

    Awesome channel! I just bought your book too!

    • @statquest
      @statquest  9 місяців тому

      TRIPLE BAM!!! Thank you very much for supporting StatQuest!!!

  • @muntazirabidi
    @muntazirabidi Рік тому +1

    Thank you. Wonderfully explained!!

  • @JeanLouisKali
    @JeanLouisKali 4 місяці тому

    This is the best explanation I have ever come accross on Linear Regression. I have a much better intuitive understanding of what the mathematic formulas I was exposed to mean. I do have a question. At 21:42, should the numerator be interpreted as [SS(mean) -SS(fit)]/(Pfit - Pmean) or is it SS(mean) - [SS(fit)/(Pfit - Pmean)] ? The position of the square brackets is not clear to me. Kindly clarify.

    • @statquest
      @statquest  4 місяці тому +1

      It's the former. It should be [SS(mean) -SS(fit)]/(Pfit - Pmean)

  • @krishnendusinha4409
    @krishnendusinha4409 Рік тому +3

    Your videos are awesome! Thanks a lot for making complex concepts simpler. It will be helpful if you clearly explained Discrete probability distributions

    • @statquest
      @statquest  Рік тому

      I cover the binomial here: ua-cam.com/video/J8jNoF-K8E8/v-deo.html

  • @isaachiew4906
    @isaachiew4906 Місяць тому +1

    Hi there, is there a playlist compiling a list of videos of yours relating to machine learning?

    • @statquest
      @statquest  Місяць тому

      Yes, you can find everything (including playlists) here: statquest.org/video-index/

  • @khoiphamang4166
    @khoiphamang4166 Рік тому

    I have a question, in 5:24 why the variance is calculated dividing by n instead of n-1, I thought all the observed data points are just a sample of a bigger population includes data points which we haven't observed yet. I'm sorry if my English confuse you because it isn't my mother tongue

    • @statquest
      @statquest  Рік тому +2

      In this context, the way we use variation means that denominator will cancel out, so it really doesn't matter which one (n or n-1) we use.

  • @umasingh3601
    @umasingh3601 5 місяців тому +1

    Best explanation ❤

    • @statquest
      @statquest  5 місяців тому

      Thanks a lot 😊!

  • @B-hooktuber
    @B-hooktuber 8 місяців тому +1

    Cool merch you could probably easily create would be a workbook to pair with your book where we could practice calculating R2 for exemple in different scenarios. That way, everytime you learn a new concept you can practice doing the formulas :) i'd totally buy that 😏 and maybe links to extra videos or explainations on the concepts that are a little harder to comprehend for people that are completely new to this field and a little slow lol(like linear regression 😅)

    • @statquest
      @statquest  8 місяців тому

      That's a great idea!

  • @lynnamanda4093
    @lynnamanda4093 Рік тому +1

    Thank you so much Josh !

  • @simplemindedperson
    @simplemindedperson Рік тому

    Thank you for the nice video! I wonder for your explanation to the F curves around 25:53, shouldn't it be (p_{fit} - p_{mean})=1? In addition, would you please provide the link to your video about the degrees of freedom if that is already available?

    • @statquest
      @statquest  Рік тому +2

      Yes, that is a typo. And, unfortunately, I haven't made the degrees of freedom video yet. However, it's still on the todo list.

    • @simplemindedperson
      @simplemindedperson Рік тому +1

      @@statquest Thank you! I look foreward to your new ones

    • @jix8874
      @jix8874 11 місяців тому +1

      @@statquest looking forward to the degrees of freedom video too!

  • @에헤헿-l7v
    @에헤헿-l7v Рік тому

    I don't understand why least squares can cause any term that will make ss(fit) worse to be multiplied by 0. Is it because mean squares differential the equation?
    15:20

    • @에헤헿-l7v
      @에헤헿-l7v Рік тому

      or is it because things like ridge regression can shrink the coefficients to 0?

    • @statquest
      @statquest  Рік тому

      Least squares minimizes the sum of the squared residuals and if setting a parameter = 0 reduces the SSR, then that's what will happen.

  • @muhammadomarkhayyamkhan3593
    @muhammadomarkhayyamkhan3593 7 місяців тому

    Your explanations are wonderful. Please just recommend the book should be studied with your videos. Please make videos on chi-Squared distribution, Monte Carlo Simulations and Hypotheses testing.
    Thanks for your valuable help.

    • @statquest
      @statquest  7 місяців тому

      My favorite book to go along with my videos is The StatQuest Illustrated Guide To Machine Learning. You can get it here: statquest.org/statquest-store/

  • @blahblah_06
    @blahblah_06 Рік тому

    Around which point do we rotate the line ????????
    Beautiful lecture..really easy to understand

    • @statquest
      @statquest  Рік тому

      There are two different ways to fit the line to data. The one most commonly used is to simply do the math and solve for the optimal fit (take the derivative with respect to the squared residuals and solve for where it is equal to 0). However, that method only works in this specific situation. A more general method is based on the "rotate the line approach" that I illustrate in this video. To learn more about it (how to rotate the line), see my video on Gradient Descent: ua-cam.com/video/sDv4f4s2SB8/v-deo.html

  • @prithvidhyani2002
    @prithvidhyani2002 9 місяців тому

    Great video overall! But I'm a little confused with your description of calculating a p-value for the R^2. Does this mean we are treating R^2 as a random variable itself and looking at its distribution? Because to me it seems like it is the f-statistic that follows an f-distribution, hence we are calculating a p-value for the f-stat, not the R^2 itself, which(correct me if I'm wrong) does not follow any specific distribution. So what exactly is the connection between the R^2 and the f-stat and its corresponding p-value?

    • @statquest
      @statquest  9 місяців тому

      The f-statistic is what we use to calculate the p-value for the r-squared.

  • @toribentley2409
    @toribentley2409 4 місяці тому

    this is amazing, thanks a lot @statquest , please can you also do a video of linear mixed models and generalised linear mixed models, there a few videos about them on UA-cam, it would really helpful. Thank you for the good work

    • @statquest
      @statquest  4 місяці тому

      I'll keep those topics in mind.

  • @Jason-o5s
    @Jason-o5s 4 місяці тому

    Cheer~~~arranged in or extending along a straight or nearly straight line.😊

  • @gnosmik
    @gnosmik 2 роки тому +2

    This is an excellent video Josh, thank you! I understand all well until you explain about p-value 23:58. So we were using a dataset of mouse size/weight and weight/tail length/body length, but I'm confusing where the 'random dataset' comes from when you calculate p-value. Could you explain a bit further about this please?

    • @statquest
      @statquest  2 роки тому +6

      The idea is to give you an intuitive sense of what the p-values associated with linear regression represent. So, to start with, we had 9 data points (9 pairs of weight/height measurements) and fitted a line to it and calculated the F value. That is the "observed" F value generated from the original, raw data. Now pair 9 random values for height (and these could be any reasonable values for height that you randomly select) with 9 random values for weight (and these could be any reasonable values for weight). Calculate the F for those pairs of random values and put that in a histogram. Then repeat until we've done that a lot of times and compare the observed F value from the original data to the histogram.

    • @gnosmik
      @gnosmik 2 роки тому

      @@statquest Thanks for explaining all. Much appreciate it. So those 'random values' are completely random, just made up within the range of the normal dataset, right? Then when we are calculating F and p values in SPSS or R, do those softwares go through this process? It might be a bit silly questions, hopefully I'm not too far away!

    • @statquest
      @statquest  2 роки тому +4

      @@gnosmik That's the idea. However, as mentioned at 25:26, in practice, people (and software) just use an F-distribution (which is an equation for a curved line) to calculate the p-value. The idea of using random data is just to give you an intuition of what the curved line created by the F-distribution represents.

    • @gnosmik
      @gnosmik 2 роки тому +1

      @@statquest Excellent! Thanks Josh

  • @johnlemon1595
    @johnlemon1595 Рік тому +1

    Hi josh, while getting to R^2, you give the formula y= (data-mean)^2. This contradicts your StatQuest "Fitting a line to the data", where your formula was "(b-y1)^2+(b-y2)^2+...", meaning "(intersect-data)^2. Now i already understood that by squaring the difference you get the same positive value, so the order doesn't matter for this purpose. Is there another reason why you put it in the order "(data-mean)^2" in this video?
    Thanks. Love the videos, just watching for fun

    • @statquest
      @statquest  Рік тому

      Since order doesn't matter, it's hard for me to remember to be consistent.

    • @johnlemon1595
      @johnlemon1595 Рік тому +1

      Okay great, just was wondering if i was missing something here @@statquest

  • @ashutoshshrivastava1305
    @ashutoshshrivastava1305 2 роки тому +1

    Amazing explanation

  • @lattoufj
    @lattoufj 8 місяців тому

    Hi Josh,
    Very nice video!
    Shouldn't the distances from the points to the line be a perpendicular?

    • @statquest
      @statquest  8 місяців тому

      If they were perpendicular, than we would lose the relationship between the variable on the x-axis and the variable on the y-axis, and the whole point is to use an x-axis value to predict a y-axis value. Thus, the residuals are parallel with the y-axis - this preserves the relationship that we want to use to make predictions.

  • @Tatya1905
    @Tatya1905 8 місяців тому

    What is the value n (that was mentioned while explaining the degrees of freedom)?

    • @statquest
      @statquest  8 місяців тому

      n = the number of data points in the graph.

  • @looklook6075
    @looklook6075 10 місяців тому +2

    I was always wondering why the model chooses to use R2 rather than absolute value of R, until you draw that polynomial out of all sum of squares. It makes sense now

  • @LeBlayout
    @LeBlayout Місяць тому +1

    Thanks Josh Starmer

  • @lilysun1296
    @lilysun1296 2 роки тому

    Thanks for the video. Could you please explain more why SS(fit)/(n-pfit) instead of n here 22:48? Thanks a lot.

    • @statquest
      @statquest  2 роки тому +1

      This has to do with "degrees of freedom" and one day I hope to cover that topic in full.

    • @zauraiz
      @zauraiz 2 роки тому +1

      @@statquest Looking forward to the degrees of freedom video! Parameters have always been a confusing topic for me

  • @aitorolaso1352
    @aitorolaso1352 11 місяців тому +1

    absolute masterpiece

  • @anelazikic5114
    @anelazikic5114 5 місяців тому +1

    Thank you so much for this video

  • @Slayer1407-d9d
    @Slayer1407-d9d 10 місяців тому

    Question. Why are we calculating R2 value and the p value? Is it the industry standard? Or else What led to the decision that you included it with linear regression. Theoretically Lin reg is complete before that right?(Making concepts clear)

    • @statquest
      @statquest  10 місяців тому +1

      If you just want to fit a line to data, you can used the method of least squares. However, if you want to quantify how well that line fits your data, then you use Linear Regression. Linear Regression consists of using least squares to fit the line to the data and then calculating r^2 and its p-value to evaluate how well that line fits the data.

    • @Slayer1407-d9d
      @Slayer1407-d9d 10 місяців тому

      @@statquest still confused.. as you said 'how well it fits the data', so the r2 and p value are tests for evaluation right? dont they have alternatives? or is it necessary to do exactly these steps. I'll still get a logistic regression model but it may not be the best one without them?
      Or are you saying that these, or some other alternatives tests are necessary to do, to assess the model and this repeats iteratively until best fit?

    • @statquest
      @statquest  10 місяців тому +1

      @@Slayer1407-d9d They do have alternatives, so, as you say, you might think of r^2 and its corresponding p-values as the 'industry standards'. Pretty much every program that offers a linear regression function will give you those as outputs. However, there are alternatives, and you can read more about them here: developer.nvidia.com/blog/a-comprehensive-overview-of-regression-evaluation-metrics/ among other places.

    • @Slayer1407-d9d
      @Slayer1407-d9d 10 місяців тому

      @@statquest Thanks a lot for clearing that

  • @catcen9631
    @catcen9631 2 роки тому +1

    insanely good video

  • @Jiacancan
    @Jiacancan 8 місяців тому +1

    thank you. that was very clear

  • @sopeadaralegbe8077
    @sopeadaralegbe8077 Рік тому

    is residual the difference between the observed value of the dependent variable and the predicted value or the difference between the overall mean of the dependent and the observed value

    • @statquest
      @statquest  Рік тому

      The residual is the difference between the observed and predicted values.

  • @urahulk-l6k
    @urahulk-l6k 6 місяців тому

    Hello, I had one doubt. For calculating multiple F values, are we taking random samples from our original dataset itself? As in, if there are 100 data points in total, we will take 80, 70 and any random data points from 100 to plot F values on histogram? Could you please help me with this?

    • @statquest
      @statquest  6 місяців тому

      The example where we use random data is just an example of the concepts behind how the p-value is calculated. In practice, we use a curve generated by the F distribution (see 25:26) that represents what would happen if we had generated an infinite number of random datasets.

  • @kushagrastripathi
    @kushagrastripathi Рік тому +1

    Very helpful. Thank you

  • @mathematics6199
    @mathematics6199 9 місяців тому +1

    Hey hi, R squared can be negative as well right?

    • @statquest
      @statquest  9 місяців тому +1

      Not in the context of linear regression. In other contexts, though, it can be.

    • @mathematics6199
      @mathematics6199 9 місяців тому +1

      @@statquest R^2 is just a metric right, and I can set the coefficients of independent variables in such a way that variance(error) exceeds variance(y),( as variance(error) = variance(y* - y), (where y* is the infered value, and y is the actual value) , I can always make y*-y infinitely high for one datapoint, by choosing appropriate coefficients ), or am I wrong? Please correct me.

    • @statquest
      @statquest  9 місяців тому +1

      @@mathematics6199 Yes, in theory, you can do that - but that's not linear regression. In linear regression we don't just set the coefficients to whatever we want. We set them so that they minimize the sum of the squared residuals. And this is why R^2 isn't negative in this context. However, in other contexts, where you can do whatever you want, yes, it can be negative.

    • @mathematics6199
      @mathematics6199 9 місяців тому

      @@statquest Thank you so much.

  • @qaziaman8194
    @qaziaman8194 8 днів тому +1

    If you could please make a video on assumptions of linear regression, that would be helpful.

    • @statquest
      @statquest  7 днів тому

      I'll keep that in mind.

  • @javo11
    @javo11 24 дні тому +1

    Great! Thank you!

  • @puneetkumarsingh1484
    @puneetkumarsingh1484 Рік тому

    Not that it matters here but the shouldn't the sample variance formula have n-1 instead of n?

    • @statquest
      @statquest  Рік тому

      In this case it doesn't matter.

  • @JasonKaros
    @JasonKaros 2 роки тому +1

    Why was the original Linear Regression video removed for this one? Is the information of this more accurate or clearer?

    • @statquest
      @statquest  2 роки тому +13

      Without telling me, UA-cam put the original video behind a paywall, so re-uploaded it so it would still be free

  • @adone1234
    @adone1234 10 місяців тому +1

    u just earned a subcriber

  • @utku_bambu
    @utku_bambu 2 роки тому +2

    thank you for this

  • @МаксЧерн-х2л
    @МаксЧерн-х2л Рік тому +1

    Thank you ever so much!

  • @mj-gp3lk
    @mj-gp3lk Місяць тому

    why p value needs to be small?
    pls answer

    • @statquest
      @statquest  Місяць тому

      If the end of this video doesn't answer your question satisfactorily, please see: ua-cam.com/video/vemZtEM63GY/v-deo.html and ua-cam.com/video/JQc3yx0-Q9E/v-deo.html

  • @ritardstrength5169
    @ritardstrength5169 5 днів тому +1

    18:30 Is F the F distribution?

  • @theolau7335
    @theolau7335 Рік тому +1

    Very nice, thank you

  • @mmkvhornet7522
    @mmkvhornet7522 7 місяців тому +1

    thanks for the video

  • @abdullahs9500
    @abdullahs9500 Рік тому +1

    That was a really mice explanation.. Thank you!

  • @stevinbrat
    @stevinbrat 10 місяців тому +1

    you are a genius!

  • @t217265
    @t217265 2 місяці тому +1

    I'm so confused. Am i supposed to draw the squares? Where are the squares? I need help 😢. I'm never going to pass this class.

    • @statquest
      @statquest  2 місяці тому

      This video attempts to explain the concepts behind how linear regression works. However, you don't actually do these things in practice. In practice you use a program, like R, to do it for you. For details, see: ua-cam.com/video/u1cc1r_Y7M0/v-deo.html

  • @atharvigupta4250
    @atharvigupta4250 8 місяців тому

    so is mouse size a confounder?

    • @statquest
      @statquest  8 місяців тому

      What time point, minutes and seconds, are you asking about?

  • @ritubhatt7367
    @ritubhatt7367 2 роки тому +1

    I am not able to find the video 'Fitting a line to the data'

    • @statquest
      @statquest  2 роки тому

      I have contacted UA-cam about this problem, but, unfortunately, they are all on vacation until next week. :( The good news is that this video does a pretty good job summarizing the concepts in that other video.

  • @sopeadaralegbe8077
    @sopeadaralegbe8077 Рік тому

    what's the difference between RSS and SS(fit) ?

    • @statquest
      @statquest  Рік тому

      They are the same. However, I changed notation so that I could specify when which model we were using to make the predictions. SS(fit) is the RSS around the fitted line and the SS(mean) is the RSS around the mean.

  • @vatanrangani8033
    @vatanrangani8033 Рік тому

    so is R square , a correlation coefficient?

    • @statquest
      @statquest  Рік тому

      It is the square of the correlation coefficient.

  • @VirtuosicBeats
    @VirtuosicBeats Рік тому

    Awesome, but can we do this without squaring? Why can't we just sum the residuals without any squaring, it looks like it should give us the sum of all distances and then we could plot it in the same way and pick the rotation that gives us the least sum of non-squared residuals and it should still work, curious why do we choose to square it, thank you so much for the video

    • @statquest
      @statquest  Рік тому +1

      If the "distances" below the line are negative, they will cancel out the ones above them, so that's a problem. However, we could then take the absolute value so that everything is positive. This could work if Linear Regression was actually solved the way I've presented it here. However, in practice, when you square the distances, you can solve for the optimal parameters directly by taking the derivative of the squared residuals with respect to each parameter, setting those derivatives equal to 0 and then solving for the parameter values.

    • @VirtuosicBeats
      @VirtuosicBeats Рік тому +1

      @@statquest Thank you so much , it makes sense now

  • @joshuaaddo1609
    @joshuaaddo1609 11 місяців тому +1

    This is great

  • @atharvigupta4250
    @atharvigupta4250 8 місяців тому

    how do you come with the equation

    • @statquest
      @statquest  8 місяців тому

      What time point, minutes and seconds, are you asking about?

  • @ajalanbrown2200
    @ajalanbrown2200 10 місяців тому +1

    i had to like just because of the song

  • @alabenmed4661
    @alabenmed4661 2 роки тому

    hello i love watcing your video they are entertaining and educaional but i saw some other videos of ways to determine intercept and slope of a line
    im wondering if you have a video about that or is there a better approach ?

    • @statquest
      @statquest  2 роки тому +1

      There are a number of ways to do it. One is to use an analytical solution. Take the derivatives of the equation with respect to the different variables (in this case, the slope and the intercept) and then solve for when those derivatives are equal to 0. For linear regression, this is a fine way to solve the problem, but it only works in this one case. A more general solution is to use something called Gradient Descent. This works on regression problems and many, many more. For details about Gradient Descent, see: ua-cam.com/video/sDv4f4s2SB8/v-deo.html

    • @alabenmed4661
      @alabenmed4661 2 роки тому +1

      @@statquest thanks man have ag reat day

  • @hoanglexuan7861
    @hoanglexuan7861 10 місяців тому

    can you do Quantile Regression?

    • @statquest
      @statquest  10 місяців тому

      I'll keep that in mind.

  • @НиколайНовичков-е1э

    Thank you :)

  • @streampunksheep
    @streampunksheep Рік тому

    I am going to statquest Isle!~

  • @adone1234
    @adone1234 10 місяців тому

    its like years since u uploaded this

    • @statquest
      @statquest  10 місяців тому

      I know! This one is classic! It might even be "pre BAM!"

  • @Phi_AI
    @Phi_AI 6 місяців тому

    This is implementation of Linear regression from scratch in NumPy only. In-depth explanation of key concepts like Cost Function and Gradient Descent
    ua-cam.com/video/wxCQxZKo4hU/v-deo.html

  • @dead_again9839
    @dead_again9839 3 місяці тому +1

    this is fucking fantastic

  • @exarchoskanelis84
    @exarchoskanelis84 2 роки тому +1

    Legend

  • @demalegabi
    @demalegabi 2 роки тому

    I think at ua-cam.com/video/7ArmBVF2dCs/v-deo.html the slide meant to say (SS(mean) - SS(fit))/(p_fit - p_mean) for the numerator?

  • @dklc28
    @dklc28 14 днів тому

    it was great at first and then i lost track after 19 minute mark

  • @prachirahate1631
    @prachirahate1631 10 місяців тому +1

    awesoommeeeeee!