3.2: Linear Regression with Ordinary Least Squares Part 1 - Intelligence and Learning 

I have linear depression

my ridiculously expensive college course can't even get close to the brilliantly entertaining and succinct way you describe things at 1.75x speed haha - thank you so much!

Subbed for multiple color markers.

"I'm really sorry, I'm going to do this in Fahrenheit, I have to apologize for that. I'll happily say "maths" though." You crack me up Dan

Great explanation. You're the only channel that has such a nice balance between explaining academic content and programming it.

Nice job re-capping the marker as you said "recap" at 14:22.

Dan, you are precisely the one, that our education institutions currently need, simply amazing way of making anyone understand even the most complex stuff

Nice video! The numerator of the expression for the slope is actually the sample covariance of X and Y. Sample covariance is a measure of linear dependence. The denominator is the sample variance of X. So the slope is loosely said the linear dependence of X and Y, normalized by the variability in X. Hope that makes sense!

ordinary least Square .. Very well explained Sir :-) ... i am preparing for data science as my carrier ...

I am smiling now...I was very confused till i watched your explanation. Thank you Sir!

6 years later and this content is helping me out

I wish you had a teacher like yourself. If I were to compare this video to the entirety of what I learnt from my "programming" classes, I'd say I have wasted too many hours in said classes.

Thanks for the video. finally easy explanation of linear regression.

Please BIG Please, continue with this series. I've followed along with your genetic algorithms, and now I'm busy with neural networks, so please continue with this. Would really appreciate it.

Great job! This is the nth video of yours I've watched and you've been able to explain hard concepts like AI algorithms like they were nuts! It seems they're so easy and I don't know if you're too good to explain or I'm so dumb I'm not catching the things right.

You’re one of my heroes, man. Seeing you make these coding videos years ago inspired me to learn new languages and technologies. Playing with P5.js is lots of fun.

You are the best teacher I've ever had. Seriously. And I've had a LOT of them.

heehhhe.. bro honestly you have win my day. your sense of humor makes me understand it greatly. congrats again. hehe

Great work sir, You have an art of teaching with fun.

I wish I had teacher like this.

You are just awesome. ..so intelligent yet humble.

Very neat explanation, explains the basics very well. Keep up the good work :)

Bro, this is so much fun to learn.. Thank you.. you explained it very well.. you really deserve a like and a subscribe

It all makes sense now thank you for saving the day and you make learning fun :)

With this level of hotness he can teach me anything 🔥

Thanks for the video. your demeanor really brightened my day.

After googling for what I needed to know to do my project I have ended up on this video and channel learning about OLS. Although it did help me to understand better what is OLS I do't think I can do this on my own. It would be cool if anyone from the comment section or Daniel could help me out with my problem. So, I'm trying to create a math solution that would give me soccer players post game ratings based on the actions done during the game. It seems that googling is keeping me in a loop around Linear Regression, as it seems that such math model has been used, in combination with some others, to do a real life predictions and post game rating for soccer players by various online sites and soccer journals. The system I would like to create, first and foremost as a math model and then later as an actual code, would be fed by 30+ events (goals, assists, block, saves, etc) that should quantify all of that as a number on a scale from 1 to 10 with 2 decimal points as a precision. Is OLS the right way to go? Perhaps other Linear Regression model? Maybe totally different math model and a formula? Where do I event start when I do pick a model? Decide how much of these actions are worth and then fit them in the model? Any help would be great. Thanks.

Amazing video - Your videos are the best dumb (dumb being me) it down versions I have found in ML. Thank you very much

one of the best explanation on linear regression! thank you!

I was having trouble understanding this. Thanks to you I get it now!!

his vibes are off the charts

Presumably you either want to go from i = 1 to n in x_bar, or divide by (n+1), since there are n+1 terms in that sum (from 0 to n)

Thank you AP Stat. I actually understood all of this

u make math interesting for ur student..good job sir

Great stuff as always! I appreciate you covering this statistical content :)

I already said this, but this man is gold

Wow. You're awesome. I was able to understand linear regression with your video.

Oh. Oh wow, I never saw it when I actually studied stats but it looks like this is where the i=0 to n loop counter convention comes from. If the relationship isn't that direct it's still very similar and helps my understanding.

"I head there's this channel, with tutorials and a whiteboard, where they use multiple colours". Check out blackpenredpen.

Thank you so much,this lecture has become really helpful to me

In the uk our general equation of a line is y=mx+c. Whichever country changed it is just petty 😂

@11:17 "...all of the X-files[viles?], values..." lol Just shows how your brain is always making connections everywhere! Great videos! Your stuff always makes my day :)

Great explanation! Super straightforward! 10 / 10 !

I heard this guy used multiple colours. Subscribed.

You're awesome! I love your videos, they're always really interesting ! Big up from France :p

not sure i understand how the final slope formula (m) arrived. formula for a slope is rise/run i.e. (y2-y1)/(x2-x1). how did we get the value of slope as the final formula shown as summation

it gives degree of freedom to move the line-up and down when plotting on the line using data points

Squaring the values also has a different effect. If the line is somewhere between two points and you don't square, it doesn't care where the line is, the distance is always the sum of the two points. If you take the square though it changes that. Let's say there are two point 10 away from each other. The line could be directly on one of these points, the total distance is still 10 to the line from both points but the sum of the quare distance is 100. If the line is directly in the middle you have two times a distance of 5. Again just sum of distance is 10 but the square distance suddenly just ist 2 * (5 ^ 2) which is 50. That's why squaring it makes sense. 6:50

Needs more "this."

I just ❤ love your energy!

awesome video. thank you for sharing your knowledge was well as your jokes with us. you are GREAT

If n is the total, shouldn't i run from 0 to n-1 ? Otherwise, great videos and attitude ! Subbed.

Amazing presentation, Thanks!

fun learning with you always :)

Sir your videos are amaizing.

You're an awesome teacher!

Thanks for this video, you are really good

I would love to have you as my lecturer for all my units. You have a gift in teaching

Your videos are great❣ I'm new to ML Can you please rearrange the series for ML so that it is not messy please

Thank you so much you saved me

there's already a channel on RU-vid that is called "blackpenredpen" and he uses black and red markers to explain math

i have an idea : sometimes you write off the board so to make sure that you don't you could just draw a line to mark the limits of your draw-maths zone ?! (it would ony work if you place your camera always at the same place) =p PS : i love what you do =) please carry on !!! =D

awesome I needed this

It was very helpful

What a freakin great video :D Thank you!

This guy is legit bruh

AMAZINGGG So helpful sir .Thank you sooooo much

Awesome video! Entertaining. Keep up the awesome job =)

U are a great teacher ❤😂

I ressubed for the multicolored markers. Defenatly didn't unsub earlier just to do this. Most defenatly not.

I reallly enjoy your videos, you are really amazing

My man, you're a beast!

I become the fan of your way of teaching :) Do you have any online courses on Udemy?

You should try an LSTM for regression, since they are good for time series data

Could you please make a coding challenge where you code a cylindrical coordinate simulator aplet? The aplet should be in 3d and have sliders for adjusting the radius, angle and height. It should be entertaining and cool to program

wow you are great man keep going like this :)

I need to relate the data points to the best fit line in terms of land surveying where the data points are perpendicular to the best fit line. This is true for land surveying where the data points represent property corners and would be left or right of the best fit line. Your video shows the data points directly south (Y-axis) of the best fit line. How do I relate your example to my needs?

very nicely explain :)

Great teacher, everything is the best...Will you makr anything in C++ because you said in livestream you know it. But, can you makr an OO C++ Serial? I am really good in C++, but I can't understand classes, because I don't know why not to write single void, instead to make a full class. Can you please do something in C++?

nice video..liked it a lot

Love it 😂 04:17

Its "mx + c" where m is gradient b is y intercept

Wouldn't you square the values because if you have 2 points and you want to find the point where the distance to each point added is smallest, it doesn't matter where you try the point as long as it is on the line connecting the points. If you square the distances, however, the longer distances will count for more than the small distances (I think you know what I mean) and the added distance will be different. Otherwise, it would use less memory and make the program faster if you just took the absolute value. Thanks!

Thanks. Keep it up.

Looking forward for next videos on this subject!

If the difference is positive and negative then wouldn't adding them up minimize the residual value? Why square them?

If you calculate the sum (for x or for m), shouldnt it always be from 1 to n instead of 0 to n?

Hey! I'm looking for some fun challenges in javascript, do you have any challenges you'd recommend? p.s. I watched the live stream in which you made this video, and you mentioned Tetris. I made it in like a day, so you probably can in one video :P Would be cool to see you make it!

OoooKKKK, I got a sudden shocked by the opening casual kiddy music...

Intead of using square values of difference between the predicted value and observed value why dont we take absolute value of their difference?Please tell

I hate economics but I like your lecture. Thanks!

I passed two courses about econometrics, and just realized why it is called " ORDINARY LEAST SQUARE!".

a very interesting guy

why does not the fitted linear regression line go through the origin?? why does it intercept Y axis??

Could you give a link to the proof of the slope formula ?

Why can't we do |d0| + |d1| instead of (d0)^2 +(d1)^2

But how do you know that its not a quadratic relationship or a cubic one etc.

where is the error term??

What do you have to major in college to cover this topic? Cuz this stuff is pretty cool

why do we square the distance not just use mod?