Chapter 06.04: Lesson: Nonlinear Regression with Transformed Data: Exponential Model

[@waimyokhing]

For this exponential model how to solve > please!

[@numericalmethodsguy]

You will need to start with the sum of the square of residuals and minimize with respect to a, b, and c. You will get three nonlinear equations to solve for a,b,c. Is this model related to a real-life physical problem? mathforcollege.com/nm/topics/nonlinear_regression.html

[@AndyWicks]

This is EXCELLENT. The presentation is clear, logical and slow enough to follow. Now, I just wish my calculus had not wandered off into the sunset ... A definite thumbs up. Thank you :-)

[@AndyWicks]

Apologies for using you as a resource. I have a form of the dose-response curve where y = a + (be^cx^2) for which I need to find a, b and c. Does that reduce to ln(y) = ln(a) + ln(b) + cx^2? Again, apologies for taking your time. Andy :-)

[@profautarkaw]

Mistake is ln(a+b) is not equal to ln(a)+ln(b). You will need to start with the sum of the square of residuals and minimize with respect to a, b, and c. You will get three nonlinear equations to solve for a,b,c. Is this model related to a real-life physical problem? mathforcollege.com/nm/topics/nonlinear_regression.html

[@rehabmokidm7252]

first, thank you for this video, it's really helpful. second, i am trying to carry out a nonlinear model for a lithium-ion battery to predict the lifetime, any recommendations?

[@edwardbush4364]

Is there a video that you have done that explains how you get the linear model regression formulas seen at 6:17?

[@profautarkaw]

yep, see videos 3 and 4 at nm.mathforcollege.com/topics/linear_regression.html

[@saifullahgarbayaro7805]

For exponential error model, please can you tell me why 2 and 10 are chosen in this equation :w alpha, i=2^-alpha i X 10. Sorry for the expression

[@sebasgolem4411]

I dont see the importance of the 6th and 7th slide, can some explain me where do these formulas are used further along

[@numericalmethodsguy]

Those slides pertain to if one was not transforming the data. To see what happens if we do not transform data, look at videos 6, 7, 8 and 9 at nm.mathforcollege.com/topics/nonlinear_regression.html

[@ggwpjd9826]

Is there another video showing the proof of why derivatives from slide 6 are without doubt a minimum and not a different type of stationary point?

[@numericalmethodsguy]

See the appendix of this. nm.mathforcollege.com/mws/gen/06reg/mws_gen_reg_txt_straightline.pdf The first derivative test is only telling us that it is a local minimum or local maximum or an inflection point. The second derivative test in this case will point it to be a local minimum. And since there is only one solution from the first derivative test, it has to be an absolute minimum. See the appendix.

[@muratcanakdogan26]

What is the solution of the following equations by data sets Y=(A)/(x+B) and Y=(1)/(ax+B)²

[@pubududara883]

thank you, this was really helpful

[@amalik1171]

Sir ln(e^bx) =b, not bx

[@numericalmethodsguy]

How do you reckon that? ln(e^(2*3)) is not equal to 2. Is it!

[@Ayberkoski365]

W O W

[@vijayprabhakaran453]

Your definition ( which was absent except for some examples) of Non Linear Regression is wrong !! You state at 1:14 that the polynomial model as stated is a non linear regression model , it is not , it is linear in the parameters to be estimated!!! Terrible