Least squares line (KristaKingMath)
Вставка
- Опубліковано 11 лют 2025
- ► My Precalculus course: www.kristaking...
Learn how to find the equation of the least squares line, also known as the line of least square, the regression line, or the line of regression. Given several coordinate points, use formulas for m, the slope, and b, the y-intercept, to calculate the equation of the line that is the average of all the points.
● ● ● GET EXTRA HELP ● ● ●
If you could use some extra help with your math class, then check out Krista’s website // www.kristakingm...
● ● ● CONNECT WITH KRISTA ● ● ●
Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingm...
FACEBOOK // / kristakingmath
TWITTER // / kristakingmath
INSTAGRAM // / kristakingmath
PINTEREST // / kristakingmath
GOOGLE+ // plus.google.co...
QUORA // www.quora.com/...
I don't understand why they teach this so darn difficult when she's literally made it so damn easy to understand.
I dont mean to be offtopic but does someone know a tool to log back into an instagram account?
I stupidly forgot my password. I love any help you can give me
@Raiden Maurice instablaster ;)
@Korbyn Carson I really appreciate your reply. I found the site through google and I'm in the hacking process atm.
Seems to take a while so I will reply here later when my account password hopefully is recovered.
@Korbyn Carson It did the trick and I now got access to my account again. I'm so happy!
Thanks so much, you saved my account !
@Raiden Maurice You are welcome :)
I tried Khan Academy and I even tried going to my professor to learn about the linear regression line and you have taught me more than the both of them combined. Thank you so much! You're amazing
Nobody beats Khan academy
This video is so clear. Why formulas are rarely explained in this way, I will never understand. Keep making videos!
Thank you for this explanation. My teacher was all over the place trying to explain this but you made it really simple and it's not as intimidating as I thought it would be. Thank you so much and keep up the great work with your videos!
I'm so glad I could help! Thanks for the comment. :)
I just watched half a dozen videos on this subject and your explanation was by far the best and easiest to understand! Thank you for taking the time to help those of us who struggle with math.
I'm so glad you liked the video! I'm happy I can help! :)
Math is the one thing that gives me anxiety and your calm voice actually helps me freak out less.
Awww! I'm so glad it helps!
This was so incredibly helpful. My book, my professor, other videos online, none of them made any sense to me. I'm sure you hear this often but thank you and keep up the good work!
I see what you're saying, but yes, the x-value would be the year and y-value would be the time. If you were going to write a function that modeled the data, it would be a function that models how the winning times change over the years, and you could look at a particular year to see how fast people were completing the race during that year. So it would still be a helpful function. :)
Thank you! This is very helpful. I found your videos while brushing up on math as I get ready for grad school this fall to get my MBA at UCLA. You explain very clearly, turning complex to simple digestible concepts.
Oh dear lord. Four hours later and you shed so much light on this concept.
I'm so glad it helped! :D
You're welcome! Glad I could help. :)
my god, you are a gift! Struggled with this for months, Your explanation is brilliant and your presentation is so clear and concise that it makes me wonder why I haven't been able to get this til now. Keep up the awesome work!
Thank you so much! I'm so glad the video helped make it clear!! :D
integralCALC If only I could find someone to explain the math behind calculating the coefficient of a 6th degree polynomial trend line - by hand - I would feel that I have actually learned something....!
You saved me every semester. Thanks a lot. :D
You are a really good teacher.
I'm so glad I could help along the way!
YOU.ARE.A.GODDESS. I have my third exam tonight and my professor taught us the most complicated and long-winded process for this. This literally takes less than 3 minuets and less space on paper. I needed to get an A on this exam. YOU SAVED MY COLLEGE CAREER. I love you soo much. I mean seriously, You are my Jesus Christ.
LOL, I love you too! :D I'm so glad this helped, and I hope you did GREAT on your exam!! :D
Aced it with flying colors. Thank you.
LazyGirlsClub Yay!!! Thanks for letting me know. :)
Thanks for the comment! Glad you liked it. :)
This tutorial was SO very helpful!! Complicated equation made easy!! Thank you so very much!! Not to mention her voice is very soothing so you want to learn it!
Thanks, Paige, so glad it helped!
You're so welcome!
you're welcome!! i'm so glad it helped!! :D
I'm so glad it helped! Thanks for letting me know. :)
Huge help! way better than my professor. Its always easier to learn coming from a pretty face as well
I'm a CS major struggling with I a high performance software class and this has helped me so much. Thank you!!!
you're welcome! i'm so glad it helped!!
I'm so glad I could help! :)
this is the first time in my life I actually understood this concept. thanks a lot.
this was great! i just started a stats 2000 class and was totally lost on how to find the individual values to plug into the equation y=mx+b, thank you!
Thank you so much for making the video. I now understand the equation because of your help.
You saved my life, my basic statistic teacher keeps killing me. Thanks Krista King.
+James Young You're welcome, I'm happy to help!
I don't know why but you seemed to discuss it on a really light-tone manner. It barely felt like a lesson coming from you. Thank you for this and cheers!
:)
Awesome! Glad I could help refresh your memory. :)
I'm so glad it made sense! :D
Glad you liked it!
You deserve an award. Thanks 😊
Best teacher ever
You list several names for this line, except my fave -- the line of best fit.
crystal clear!! thanks so much for making this video with your clear voice and instructions:)
Hi, krista. You are a wonderful teacher
Loved it, one of the most basic and simple explanations I've come across. Thank You Krista
Glad you liked it!
Your beauty is captivating, but I also appreciate your helpful videos. I couldn't understand a single thing off my Statistics book.
Glad you liked it! :)
this video just saved my life!!!! Very helpful thank you!!!
Different from how I learned in class but worked much better for me! Thank you for a finals review!!! :)
Glad it could help! :D
Thanks! For all you have done, we here in Brazil needs you. I'm in first year of Mathematics graduation.
That's so sweet of you to say! I want to visit Brazil someday. :) Good luck with the rest of your first year!! :D
ty so much maam krista for this genius of yours it really understand me so much i love u
I love you too!
So we meet again great one! Thanks for all your help, you are the best.
LOL, you're welcome! :)
I'm in my fourth year engineering and this is something I needed to know for an assignment but couldn't remember how to do, this helped a lot!
Thank you so much. We have quiz tomorrow in Mathematics in the modern world and you explained it clearly.
Happy to help, Nathan! I hope the quiz went great!
Thanks Krista!
Glad I could help! :D
Thank you Kristaa!
+Trinity Trev You're welcome!
ooooohhhh .... mmmyyyyyy.... Gooooddnnnneeeeesssss...!!!!!!!!!!!!!!!!!!!!!!! .......... GOD BLESS YOU................... SOOOOO MUCH .... u have no idea what you have just done for me...... life saver .....!!!!!!
+eric mjumi You'rew welcome!! I'm so glad it helped!
wait I translate what eric just said ... 'OMG you're so sweet and lovely' ... :D :D
Thank you for breaking down the formula.
Thank you so much!! I was so lost but now I get it.
You the supper star, you helped me very much in 2020
HI, You explain concepts nicely, nice way to recall the concepts :). I think least sqare line formula (in other words regression line formula) can be remembered easily using following notation
(mean(X).mean(Y) - mean(X.Y)) / (mean(X).mean(X) - mean(X.X)). As you could see both numerator and denominator is in the same form (called as covarience with respect to each other). so remembering will be easy (solves both remembering of covarience as well as reggression line formula). once we have this as m (slope) from above formula just substitute m for b = mean(y) - m. mean(X),,,,, Ola... we know know least square line's equation, we know covarience equation. (sorry, was unable to use x bar notation, otherwise it might have been much neat)
Thanks, was well explained and simple
+Adam White You're welcome!
you laid it out very clearly and were super easy to follow thanks a bunch!
You're welcome, I'm so glad it helped!!
Thanks dear ...well done.
You've saved my ass in calculus, and now in statistics!
Oh good! I'm so glad I've been able to help!! :D
Krista King I hope you really understand how much you help. It’s one thing to help one person out, but to go out of your way and make videos to help millions of people, that’s a whole other level! Not just anyone can be a good teacher, and you are great!! Keep up the good work, and I always recommend your page to people taking math classes!
Thank you for your help.
I got nothing in class but in your class I have grabbed the whole thing..thanks
No problem, Francisco, I'm so glad it helped! :D
Thank you so so much, you gave such a wonderful explanation. thanks thanks thanks
Glad you liked it!
What do I do if the data I have resembles a quadratic relationship. How do I find coefficients in quadratic least square fit?
This really helps for my final maths paper tomorrow. Thank you🙏🏽
You're welcome, Jael! I hope the final paper went really well! :)
Very helpful! Thanks.
God bless you. Could you tell me where did you get it ? .I want to understand how does it invent.
Please post more videos on Statistic .... Standard deviation... Please?????!!!!!! You are fantastic
THANK YOU, Krista! Keep up the good work, ;).
Thanks. 😊
my mid-semester exam is 2moro and u just saved my life !!!
Good luck tomorrow! :)
Great job of explaining! I do have a request though. I was wondering if you could do an example of Spline Interpolation.
YOU ARE AWESOME! Can you come teach at WSU!? You explained it so clear! Thank you
I'm not going to be able to make it to WSU, but I'm so glad this helped!
You're welcome!! :D
that was a very pretty and brilliant lecture but you don't need to combine the formula for calculating B and for M. when lecturing you need to make sure as if you're teaching to people who are completely don't know. otherwise, you're a great lady. GOD BLESS YOUR HAND
I look everywhere i could but couldn't find any answer except here. Thank you very much
You're welcome! I'm so glad I could help! :)
Keep up the great work . thank you
Thank you. Very big help!!
What software do you use to write like this?! Thanks, and great videos.
Thanks! :)
Thank you tons and tons. I finally understand!
You're welcome, I'm so glad it makes sense now!
Thanks, very helpful. I would have wished however, to see a plot of the points and the least squares line in the end.
+Benjamin Aaron Degenhart Thanks for the feedback, I agree that would have been nice to add.
Video is clear ... I still got 1 question ... that how the equation you have used to calculate the 'm' derives ... do you have any proof or any idea on that ? :D
Very nice presentation. What chalkboard app did you use to create it?
I explain the process here :) kristakingmath.com/my-videos
Yaay, I finally understand this! Just need to remember it for the exam now lol, thanks! :D
+SuperSonicSpeedGuy You're welcome! Good luck on your exam!
I have to say thank you so much for posting this easy to follow video. The book I have makes the equation a little different looking and so hard to understand. Your way of solving it is fluent and 10x easier to solve and follow. Thank you sooo much. As konataGAMERZ stated it barely felt like a lesson. Your awesome
Thank you so much, I'm so glad it helped!!
Thank you...mam.... your vedio really really help me a lot.....
You're welcome, Srabonti! I'm glad it helped!
Thank you....mam... from 🇧🇩🇧🇩....
Hi life saver, Can you please make another video on how we get the intercept and slope formulas? It would be very helpful,,thankx
Hi Krista, I like your video but you did not explain how did you come to M= 33.6. Can you please explain this to me?
Wow. Incredible. Thanks
Please share the video on Moving Least Square
Clicked for hot girl stayed for knowledge. Solid video.
That was really helpful. Thanks!
I have a question. If the x values are years. like 1934, 1948, 2004 etc.. then should I take only the last two digits? Because I keep getting an answer that is not correct. But if I use the years by the last two digits then 2004 would be just 04 which would not make sense.
Maybe try to do it where, whatever the very first year is, you subtract that from each year. So if the very first year is 1934, then 1934 becomes 0, 1948 becomes 1948-1934=14, 2004 becomes 2004-1934=70, etc. :)
THANK YOU!
Very Clear! How can I sign for your teaching?
Hey, Walter! I offer full courses on my website if you want to really jump in and take it to the next level. :D
Thank You so much!!! This was very helpful!
So glad it could help Christie! :)
Thank you.
thank you so much for this helpful video :)
i really love to see you
I just got a better understanding of the formula and how it works
Awesome! Thanks for letting me know.
Thank you very much!
+colethefatcat You're welcome! Glad you liked it.
Thanks a lot 🎉
You're welcome, Jayy! :)
in the second part of the problem, you state that the square of all the X equal to 364, but how is that possible when the x = 42? When you square x, it equals to 1764. I added up all the sums for x only to get 1764 as my answer on that part and not 364
the square was outside of the parenthese