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Statistics 101: Linear Regression, Standardized Regression

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In this Statistics 101 video, we learn about regressing standardized values. To support the channel and signup for your FREE trial to The Great Courses Plus visit here: ow.ly/xVD030fiZ8S
So this video is the next in my series on simple linear regression and what we're going to look at in this video is what happens when we perform linear regression on observations or data that we have standardized? And you should remember what that is back from when we were talking about Z-scores and things of that nature. So when we regress standardized values, some interesting things become apparent that are kind of happening under the hood and I think they're pretty interesting. So let's go ahead and look at what that looks like.
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
The Great Courses Plus is currently available to watch through a web browser to almost anyone in the world and optimized for the US, UK, and Australian markets. The Great Courses Plus is currently working to both optimize the product globally and accept credit card payments globally.

Опубликовано:

7 авг 2024

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Комментарии : 107

@mandarmanik5118 6 лет назад

Brandon - I never thought Stats could be so interesting... your teaching style is not from this dimension and cannot be described in words. Love and Respect from India my friend!!

@aniadanielamiklas9005 5 лет назад

The best educational video in Stats I have found. Thank you Brandon! I have shared it with my MBA classmates!

@fazlurrahman7644 6 лет назад

Hi Brandon, you have made this Linear Regression video so simple and easy, the whole narration looks like a story of mathematics. Kudos to you. Appreciate very much for your time and efforts.

@shubhamdas6300 5 лет назад

This series is really expanding my knowledge over regression.. Great Job.. Thanks a lot !!!

@ylazerson 6 лет назад

This video is pure gold!

@auwalaliyu174 3 года назад

Thank you Mr. Brandon from Nigeria. I'm speechless. I have to plant a tree on your behalf..

@ShalabhBhatnagar-vn4he 4 года назад

Mr. Brandon, by now you know how good you are :-) Your videos have transformed my understanding of statistics and given me a super depth for machine learning. Each time I forget or in doubt, I come back here. Thanks so much!

@cloudktichen Год назад

In India we have a culture of falling at our teacher's feet as a mark of respect. Myself, via this message fall at your feet for this remarkable video. You saved me from abusing myself in the name of mugging up for the sake of the exam.

@BrandonFoltz Год назад

Stand tall my friend, you bow to no one.

@astaconteazamaiputin 4 года назад

I can't believe I see so few views for such a valuable resource ! Thank you for your effort and for the extremely good explanation in all your videos which I have seen so far. Much appreciated !

@AnshumanDash 6 лет назад

I loved going through these videos on regression. One request. You have several videos on linear regression. But they aren't numbered in the sequence it has been explained. So at times it gets confusing.

@rk2904 3 года назад

Brandon - Your teaching style is very effective and to the point. You make things easy to understand. Appreciate your efforts. God bless you

@manan43 6 лет назад

Great video, never thought stats could be this interesting :)

@daddy179 6 лет назад

Happy to see you’re back

@arahex8525 Год назад

just the videos I need. Very clear and helpful. Thanks a lot Brandon

@st093076 6 лет назад

Thank you soooooooooooooo much Your video saved me from my Statistic midterm exam 非常非常感謝!您的影片拯救了我的統計學期中考QAQ

@gcumauma3319 3 года назад

The visual narrations are really superb! Many thanks for the lecture.

@anjali_23 4 года назад

I have my exam tomorrow, I found your channel today and your videos have made everything so clear to me! A really amazing way of teaching! I'm gonna watch your more videos to learn something new! Thank you so much, @Brandon Foltz

@Azureandfabricmastery 6 лет назад

Thank you. Very interesting. clear and precise.

@ABC2691 6 лет назад

I am from the Notification Squad. This was immensely helpful. Thanks a lot from India :)

@HellenofTroy897 2 года назад

You have made stats so interesting. Thank you so much.

@mariar.suarezrozo9015 5 лет назад

Pure gold! thanks

@Himilo.Hansare 2 года назад

You are on another level. Thank you!

@claudiusandika5366 4 года назад

thank you for your teaching.. very simple and easy to understand. warm regards from Indonesia!!

@jamiebannon891 4 месяца назад

What an excellent video, thank you very much.

@kumarprateek1279 4 года назад

Thanks for these videos.

@joyswebilius2492 5 лет назад

Dear Dr. Foltz, I'm paying outrageous sums of money to earn my PhD. in business online and you are my lifesaver! When I can afford it I will definitely send a donation to support your work.

@GeekGirl523 5 лет назад

Yeesh no doubt, eh? Tuition doesn't guarantee good quality instruction...

@ricardoafonso7563 3 года назад

. Thank you.. Progressing along.. Nice e-lectures .

@zethumsindo3187 6 лет назад

Thank you Brandon from South Africa

@ebrutorun4931 3 года назад

you are perfect. Thanks to you, after 2 years, ı understand the logic and ı don't have to memorise all of these formulas. I can write them just using my mind :D thank youuuu.

@kayahmirnah7488 3 года назад

Thanks a lot. you have saved my life.

@theresemeyer9927 5 лет назад

hi brandon! can you please make a video or two on generalized linear models?

@AmitSingh-nw5yh 2 года назад

Amazing!!

@doziekingsley1322 3 года назад

Well explained teachings on regression; I found the knowledge insightful. Do you have any video series on Neural Networks?

@Diego-ck9zl 4 года назад

Amazing!

@Adluminous Год назад

Love your videos and they are so easy to follow with relevant examples however just one piece of feedback when you're explaining in your videos the explanation text has big formats and therefore blocks the visibility of the graphics in the background.

@gracendunge9212 Год назад

You are a blessing! Love from kenya

@BrandonFoltz Год назад

I am blessed to have you as a viewer Grace! My love back to you and Kenya!

@Rahul-or9hr 4 года назад

Hi Sir, your video are best . As a lay man i can understand everything. Great Work. Super Videos Could you please advise if you have machine learning course as well?

@pascalpascala6760 4 года назад

Brandon - at 3:46 The standard deviation for the independent variable X should be the Sample standard deviation (sx) instead of the population standard deviation (sigmax) since the data is sampled. Also, the standard deviation of the dependent variable Y should be sy at 5:25 for the same reason.

@BrandonFoltz 4 года назад

Hello! Thank you for your comment. Yes if this were an actual problem we would standardize each variable based on the sample standard deviation. I think in this video I was going for the underlying concept of standardization and treated the values as a very small population. Goal was to get the concept across more than anything. Thanks again!

@amirrahimi212 3 месяца назад

thank you mr brandon

@st093076 6 лет назад

Thanks a lot from Taiwan

@LaurenG191 5 лет назад

Hi Brandon! First of all, THANK YOU for these amazing videos. I've watched a lot of stats tutorials and these are by far the most helpful. I appreciate the pep talk at the beginning too :) There were a few things in this video that confused me: 1) Where does the correlation value of 0.866 come from? I thought the slope was .146, which you mention at 10:01. 2) What is the Pearson correlation used for in this example? Is it for standardized values specifically? Is there any reason to believe it would be different from the 0.866 that was calculated somewhere else? I've watched these videos in sequence, but it feels like I've missed an important point somewhere. In any case, thanks again for all of your hard work here. It's very helpful.

@manojg1981 5 лет назад

at 11.34 you will see r being calculated which is correlation coefficient.

@rikishipattu 5 лет назад

@@manojg1981 correlation Co-efficient is SQRT (Co efficient of determination) => sqrt(0.749375) = 0.86566..

@MahalakshmiDV 4 года назад

Wonderful

@wahidrahman3199 6 лет назад

thk u sir :)

@pragun1993 5 лет назад

So, for any given data with a set of input variables and output variable, the regression line will always have 0 intercept when it is plotted for standardized values and the (coefficients)betas of x1, x2, x3..xn will be correlation coefficient between xi and y? In that case how did the machine help in building out the model or plotting a best line if the regression line of standardized values has just correlation coefficients which are directly calculated with a formula?

@ericaltf4 5 лет назад

If you are trying to find the original regression slope in a logistic regression is it done the exact same way? The SD of y would just be the standard deviation of the 0s and 1s?

@winstonloke2860 4 года назад

Regression is an amazing tool.

@edumeonlinetutoring5535 2 года назад

Thank you millionsss for the videos.. Just have a question! Is it OK if I let excel do this for me? Or shall I check if what excel does is exactly the same as manual calculations???

@soroor1682 2 года назад

I should share your channel with my instructors, so hopefully, they learn how to teach and not just read those wired notations!!

@palashmyaccount 5 лет назад

Hi. Are we assuming that bill amount and tip amount are normally distributed? If we are, what happens in the case when variables are not normally distributed?

@blaine6000 5 лет назад

I was asking myself the same question. Hopefully someone can comment on this with some more info.

@sirajss1996 6 лет назад

Just in time for my exam

@surajsuji1110 4 года назад

Best

@rafibasha4145 2 года назад

Hi Brandon,@5:17 ,in case of Std normal distribution std value is 1 right so how come meal 2 has 1.5

@amirrahimi212 3 месяца назад

tnx

@NeerajKumar-vb9xy 5 лет назад

how 0.866 coefficient of correlation for standardized values?

@mohammedalsubaie3512 2 года назад

Dear Mr. Brandon you are magical seriously thank you very much for your efforts. I just have a little question, I calculated the sd of bill and it gives me 29 but you have it as 26.48, could you please explain how if you can? I would really appreciate that.

@soniairak80 Год назад

I think he divided with n instead of n-1 so 6 instead of 5

@MrAmericanDreams Год назад

Hello, can we make linear regression on non-parametric data?

@Illyria1989 2 года назад

Question! When we are standardizing the values, why do we use the population sd and not the sample sd?

@plannerjoy 8 месяцев назад

How was the standard deviation computed? The Excel computation for the standard deviation of x equals 11.84 compared to the standard deviation in the video of 26.48. What am I missing?

@thundergirl3600 5 лет назад

what is zx or zy 5:07

@amirrahimi212 3 месяца назад

great

@user-td3bq8sn4u 10 месяцев назад

where did 26.48 come from????? @Brandon Foltz

@Taoufikmoro 4 года назад

watching this in 2020 !

@fatimaqazalbash7444 5 лет назад

How did u get 0.866

@huzaifagamer1750 5 лет назад

i also woundering for this.may be somebodu can answer this.

@cghale3692 4 года назад

@Brandonfoltz At 7.32 how to do that co relation .....??? got stuck there. Sir, I have never heard of regression in my life but doing it in master now and your videos are helping me. Hope i can overcome this mountain.

@anton78bon 4 года назад

Same question for me also, did you got the answer already ?

@jetstalknecht7463 3 года назад

i took the square root of r2 in the previous video and got 0,865..

@a.v.a.bharatkumar5417 3 года назад

how to calculate standardized coefficients for each unstandardized coefficient in regression modeling with 1 variable or multiple variables

@jovanrumenic1607 3 года назад

How do we know how to calculate standard deviation?

@ahmadhuseynli2073 6 лет назад

Will you create video for gradient descent ?

@BrandonFoltz 6 лет назад

Maybe! If so it would be about the basics. Iterations of the parameters in simple regression, etc. I try to stick to things that are taught in most undergrad stats courses and stuff, so gradient decent would be outside of that scope. BUT I know it is important so I may get to it when I can. Thanks for watching!

@ahmadhuseynli2073 6 лет назад

Brandon Foltz I would buy that video series if you create the way you do all others

@scramah195 3 года назад

At 4:27, your choice of depicting the data as being normally distributed is completely arbitrary, correct? i.e. there is nothing in this problem that would suggest the data is normally distributed (further, z-scores alone do not make any assertions regarding the distributions of the data)

@abhiramips 5 лет назад

Hey, how did you find the correlation at 7:14. thanks!

@LaurenG191 5 лет назад

Seconded! I'm a bit confused - I thought the correlation value was 0.14 (i.e. for every $1 increase there is a tip increase of ~14 cents). Why is the value inverted here?

@mrraam2151 5 лет назад

@@LaurenG191 No, that's the correlation coefficient showing the strength of relationship between the two which is between -1 to 1. Excel regression output has it.

@yourswimpal 4 года назад

i think correlation is another subject all together.. so just assume 1 is fully correlated, 0 is not correlated at all and -1 is inversely correlated ( you can check out Pearson Correlation Coefficient )

@hendahmedbessa1724 3 года назад

what is inverse regression ??

@qasimalqasim7910 Год назад

wy do you use z instead t

@fgiegarra2177 2 года назад

Wow! That’s why regression is labaled as r^2 because if you square or multiply the coefficient to itself (correlation labeled as r) you will get the regression coefficient.. ahmmmm...

@emanuelhuber4312 5 лет назад

Why "Cozy" correlation?

@vinothh6078 5 лет назад

How did you arrive at correlation 0.866? That part alone is not clear. Plz explain

@ayushalad 5 лет назад

you got this answer?

@vinothh6078 5 лет назад

@@ayushalad correlation Co-efficient is SQRT (Co efficient of determination) => sqrt(0.749375) = 0.86566

@vulnerablerummy 5 лет назад

@@ayushalad i actually got the answer just by running a normal correlation formula on standardized score. here's my data if you wanna compare it : mean of zBill = -0.0017 mean of zTip = -0.0017 Covariance of zBill and zTip (COV zx,zy) = 1.0379 Standard Deviation of zBill (S zx) = 1.0940 Standard Deviation of zTip (S zy) = 1.0970 >>Correlation (COV/ (S zx)(S zy)) = 1.0379/(1.0940)(1.0970) = 0.8649 the number might also differ slightly due to rounding

@haslan4885 5 лет назад

mind = blown

@yoyomovieclips8813 4 года назад

In video you did not describe why do we need standardized regression?

@santoshsingh5656 5 лет назад

BRANDON THERE IS A MISTAKE IN STANDARD DEVIATION OF SAMPLE.INSTEAD OF N IT SHOULD BE N-1 THAT MAKES STD DEVIATION AS 29 AND NOT 26

@BrandonFoltz 5 лет назад

Hello! I can see what you are saying but it doesn't actually matter. The standardized regression coefficients value and standard error, overall r-square, F-value, and p-value are identical either way.

@subhajitmondal8910 5 лет назад

How you got 0.866 at 7:18 ?

@N0rmad 3 года назад

I'm wondering the same thing

@jetstalknecht7463 3 года назад

take the square root of r2

@CharlieChaplinVideos 6 лет назад

Please add this to P14

@BrandonFoltz 6 лет назад

Just did! I always add to the playlist the day after I publish. But it's there now. Thanks for watching!

@coryanders6328 Месяц назад

I'm so confused as to where these standard deviation numbers are coming from.

@winstonloke2860 5 лет назад

why is the standard deviation of the bill not 29?

@vulnerablerummy 5 лет назад

yeah, i also try to calculate it on excel, should be 29.00345

@anricogideon78 4 года назад

@@vulnerablerummy excel one uses divided by n-1, brandon uses n only

@diaconescutiberiu7535 4 года назад

So far was good (except the left point of the previous video, where SSR+SSE=SST was not ”true” and your explanation of ... don't look at just want point... made no sense to me (i'm not being rude... just stating i didnt understand what was going on there)... with this video you completely lost me. I don't understand where those bell shaped (normal distribution) were taken from, nor what did your 1,2 ..6 placement inside those charts mean... basically this video made me understand nothing :(. It's not a an observation against you but towards my lack of knowledge.