Linear Regression for y on x - Least squares method using Sxy and Sxx | ExamSolutions
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- Опубліковано 9 тра 2011
- The least squares regression for y on x is used to find the equation of the line of best fit for a set of bi-variate data by minimising the sum of squares of residuals as this video explains It uses the statistics Sxy, Sxx.
In this video you are shown how to work this out on a Casio Classwiz calculator using the statistics mode.
You can view other statistics video tutorials by going to www.examsolutions.net/ for the index, playlists and more maths videos on exam solutions and other maths topics or seek out my UA-cam channel / examsolutions
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Play his videos on 1.5x or 2x speed if you feel he's going too slow. The explanations are well worth listening to.
That's good - well done.
Hello, sir. If I am not mistaken, a graphic calculator is allowed in the Math Studies exam on both papers... Why not use the calculator to calculate the line of regression instead of using and applying all those formulas?
You Tube prevents me from placing a link here but if you go on my website check out the product moment coefficient in the statistics index or your exam module S1.
@Exam Solutions
this was extremely helpful! Thank you for creating this video!
Best video on Linear Regression! Extremely helpful!
Thank you!
Thanks
@xImMorTalxT That was not the point behind the video. I was trying to explain from first principles. Anyway, what if you don't have a calculator that can do regression?
All your videos has been great and explained in a simple manner. Thank you so much.
Absolutely amazing tutorial! Thank you very much, a great help. :)
Great Video, well explained! :)
I really need more of this, this is very helpful
honestly, this is the best and only good explanation I've seen about the least squares
Daaave s1 next week Wednesday?
Devil's Den same, goodluck 😭
Devil's Den 😭😭👎👎. I found some questions doable but some 😭. How did you find it?
love your videos you explain it so simply
Thanks from the UK
thank a lot...great clarity!
Thank you
Thanks
thanks a lot sir!
IT REALLY HELPS
Thank for creating this video, make several video, this was extremely helpful
thank you!!! was very useful :)
Cool - All the best
@marymalu09 Pleased to hear that you found it useful
very nice tutorial.. thank you.. was really helpful
Hello. Great lesson
What software are you using to crate this lesson?
It will not necessarily be the exact value as it is a line of best fit. However, I would expect an answer fairly close to the real one. Have you checked your values and is your observed value x within the lower and upper values that were in the original data table.
What previous video do you refer to at 5:53, where you explain how to find b in y=a+bx?
So nice video and its fully helped me to understand this method. thanks again
You are a legend!
Thank for creating this video, make several video, this was exatily helpful
@ExamSolutions thankkyouuu!!
An x on y graph would be used when x depends on y. For instance if x were the temperature of a cup of coffee and y the time. Then the temperature of the coffee would depend on the time it is sitting around. For y on x, y depends on x.
Never mind, I found it. Great videos, you are a life saver!
@ExamSolutions yeah i get where you're coming from. 1 question if there's a 4 mark question that asked to find equation of regression line if i simply put the values down because i worked it out from the calc would i get all the marks? or would i have to show some sort of working out??
Confused me in college, this helped a lot. Thanks!!
Impressive!!
Thank you very much!!! after reading book and watching this video, everything is clear!!! Even all those complicated equations ))
very good video!
is introductory,let appreciate you
great work, God bless you,
Super useful
Fabulous Teaching 👌
Sir, you're a saint.
Excellent video
You rock man
@ExamSolutions Okay so it's basically the letter before the "x" that should be solved as you solve your "b"?
thank you sir.
hats off to u
found it very useful
It depends on the question. The best way is to look at the exam questions on my website and watch the videos for S1 June 2010 6e and S1 Jan 2008 4c. However, this would make for a good video which I may do.
Life saverrrr ❤️❤️❤️❤️❤️❤️
thats nice presentation
Simplified and to the point.
Thanks for the feedback.
@AtoZyzzyva Yes, have you looked on my site.
i came back here to thank you ,i passed the math exam because of you ..this is one of the only two type of exercise which ive done perfectly at the exam alll the others were half finished because i did not understand them very well,so it helped the overral grade a lot!lol..i wish you could do videos about random variables,probabilities,conditional probability,lagrange multiplier ,integrals or second derivative test
+natalie shinobi Well done for passing your maths exam.
Greetings from Watford, UK
fantastic, really. you explained my whole chapter just in 14 mins. i now don't need to study that heavy book which indeed sucks. you are wonderful.
Excellent Explanation (y)
It was really helpful for me
Thanks to u I went through 2 chapters in about 30 mins
Excellent coaching.Thanks for clearing my doubts.
M.V.Apparao, Hyderabad
Thanks a lot sir...This video was extremely helpful..S1 seems to trouble me a lot,,but after watching ur videos..I found it very easy..All the credit goes to u
Best wishes to you.
How did u get those formulas ? Derivations?
Good
Thanks for the good work. It is really helpful.
Thanks
@Madsblach Yes but in place of your 'a' it will be my 'b' and in place of your 'b' it will be my 'a'.
Yes
@Madsblach yes
tks for tutorial!!!
+Dan Cacovean Thanks for looking at it.
Thank you!
+Leona Asgarpour You're welcome.
Evaluate the statement “In the model: y=a+bx+cz+e,if z=√x, where a, b and c are parameters to be estimated and e disturbance term satisfying classical assumptions then muliticolinearity couldn’t be a serious problem
Cool - another life saved.
@AtoZyzzyva Good - Hope it helps
Thank you so much Sir.
+Konark Raj Mishra You're welcome
Cool
Great video for last minute revision, or should I say on the day learning?
What does Sxy interprets?? You have said that you have explained it in previous class.. can you please post the link??
when would an x on y graph be used, and when would a y on x graph be used?
@SelasSolaris That's ok.
Hi Stuart,
I gave the final answers for the line in fractions.. is that still going to give me the marks?
Thank You Sir... I am looking for application of this method on 2 Dimensional matrices.
Please tell me how can I use Least Square Method on 2D Matrices?
Does this solution also work on y=ax+b?
Hi. How can I interpret the equation of regression?
How do you find the line of best fit without the trial and error?
Going International. Thanks
thanks sir love the way you explain. ndo livhuwa means thank you in venda.
Thanks.
Lol I love South Africans
Pleasure
@blockenfocken168 not at all.
my two thumbs up
I don't understand how the sum of the squares of the residuals/errors has to do with the final answer, being the line of y on x. I don't see how they link if the sum of the squares of the errors doesn't get included in the calculations to find the line equation. And also, what if you don't find the lowest error thing, as there may be so many options you can have to put the best fit in, does that mean you get it all wrong?
You take the sum of square residuals (which for an individual is y-a-bx, so sum up that for all observations) and then differentiate to obtain two first order conditions with two unknowns and then solve the equations (for the most simple case, ofc you can generalise to as many regressors as you want) for your estimators. And then you'll see if you do that, for the case of a single regressor, you get b=Sxy/Sxx and a=y(bar)-bx(bar). So you mathematically solve for the values of a and b that minimise the squared residuals. This is above anything expected at A level and the maths of it can be quite intimidating at first but stick with it, I think its very very hard to intuitively understand least squares regression unless you know the derivation and understand how the estimates are obtained
I have now made a video on this for you. Check out your exam board module. I hope you find it useful.
is the regression line affected by coding?
You can use the calculator to do the line of regression but that was not the point of the tutorial.
bien
MODE
STAT (2)
A+BX (2)
ENTER VALUES
AC
SHIFT
1 (Stat)
REG
A & B
-> AQA Question = 4 marks.
@ExamSolutions Why wouldn't you just use a calculator?? It's soo much easier and faster. Would i ever need to use this method in a test if i know how to do it on a calc??
I have answered a question using this method. But have to interpret my answer. the answer is y= -0.49 +0.44x . But when i try to put the data I have for x, the answer does not match what the true y is! I.E with a voltage applied (y) of 15v the current (x) is 6ma. Using my answer to to check this, the y value does not come to this.
@hamidbcu Pleasure
Chouutauuu Nanuuuu....
How would you do a problem where the line isn't straight? The line they are asking me is y = a(√x) + b
Betuel Oliva Nonlinear You can still use the exact same method. Ordinary Least squares requires that the model is linear in the parameters, not the variables
@AtoZyzzyva Cool