Chapter 06.04: Lesson: Polynomial Regression Model: Derivation: Part 1 of 2

Learn how to derive polynomial regression formula. For more videos and resources on this topic, please visit nm.mathforcolle...

[@ashutoshmishra7463]

Its like finding a diamond in a coal mine this maths video is 14 years old and has 26k views you know you are studying something deep when things like these happen in 2023

[@shrutijindal6040]

i wish you were my statistics teacher

[@numericalmethodsguy]

If the polynomial of order (n-1) is going to give you Sr=0, there is no need to go beyond that order. Even if you do, you will end up with the (n-1)th order polynomial as the goal is still to minimize Sr, and how much more can one minimize it if it is zero.

[@aryanshah6423]

In the end, you said why the differentiation led to the local minima was out of the scope of the video. However, I really want to know how it works. Any links or explanation would be very helpful! Thank you.

[@numericalmethodsguy]

See these related examples and use similar principles. autarkaw.org/2010/04/08/to-prove-that-the-regression-model-corresponds-to-a-minimum/ autarkaw.org/2008/07/07/how-do-you-know-that-the-least-squares-regression-line-is-unique-and-corresponds-to-a-minimum/

[@aryanshah5629]

@@numericalmethodsguy Thanks a lot sir

[@aminzairi51]

hello sir at the beginning of the video why do you equate "best fit" y = a0 +a1x + a2x^2 ?

[@numericalmethodsguy]

That is part of the problem statement. Generally the physics of the problem determine the regression model used. But sometimes you may want simple models for a short range, then one may use polynomial models. But how to choose optimum order of polynomial is given here - autarkaw.org/2008/07/05/finding-the-optimum-polynomial-order-to-use-for-regression/

[@kritikumari4038]

hello sir why did you take just the 1st order derivative and not the 2nd order derivative. if 1st order derivative is zero, Sr can either be maxima or minima. Sir can you please explain

[@diggy190]

How can I do a Polynomial regression for a function that has Asymptotes?

[@richagoyal2522]

Dear Sir, I am new to Statistics and your videos are really very effective means of learning. My concern is, suppose I have 3 input and one output vector (aA+bB+cC=D) then how could I obtain this equation. Should I derive combined SSE for every variable (A,B,C) and then differentiate them wrt constants a,b,c or there is some other better method. Please help

[@numericalmethodsguy]

+richa goyal Yep. See www.uv.es/uriel/3%20Multiple%20linear%20regression%20estimation%20and%20properties.pdf

[@babybae9711]

Hi the video is very helpful! Thank you for doing this! I have a question: why does m have to be smaller than n-1? Isn't n just the number of coordinates provided? Thank you!

[@CrispyCyclicCenk]

very good thank you

[@joe286]

very good explanation

[@numericalmethodsguy]

Thank you. To get even more help, subscribe to the numericalmethodsguy channel, and go to MathForCollege.com/nm and MathForCollege.com/ma for more resources and share the link with your friends through social media and email. Support the site by buying the textbooks at www.lulu.com/shop/search.ep?keyWords=autar+kaw&type= Follow my numerical methods blog at AutarKaw.org. You can also take a free online course at www.canvas.net/?query=numerical%20methods

[@numericalmethodsguy]

Using polynomial regression for asymptotic functions does not jive!