polynomial regression (2)

 

*** How can I define nonlinear trajectories in a growth curve model?

https://curranbauer.org/nonlinear-growth-2/

 

1. what is linear regression

https://www.youtube.com/watch?v=CtKeHnfK5uA

 

2. simple regression, multiple regression, polynomial regression

https://www.youtube.com/watch?v=Qnt2vBRW8Io

what are differences between these 3 types of regression in algebra

~ linear and nonlinear regression: the coefficients b, not the relationship between x and y

 

3. polynomial regression method: linear, quadriac, cubic and performed in R

youtube courses by Tom Sherratt

https://www.youtube.com/watch?v=DmYV5cma7cQ

~ draw a scatter plot first

~ should avoid overfitting

~ to test it: by graphic, by anova on SS

https://www.youtube.com/watch?v=gNkTydo6b-A

~ step by step in R studio

~ check residuals and fitted....

 

4. polynomial fits and splines

https://www.youtube.com/watch?v=bFOTmSsDtAA

differences among numbers of polynomial

 

 

5. There are three main situations that indicate a linear relationship may not be a good model.

https://www.theanalysisfactor.com/regression-modelshow-do-you-know-you-need-a-polynomial/

(1) Most important is the theoretical one.  There are some relationships that a researcher will hypothesize is curvilinear.  Clearly, if this is the case, include a polynomial term.

(2) The second chance is during visual inspection of your variables.  This is one of those reasons for always doing univariate and bivariate inspections of your data before you begin your regression analyses.  (You always do this, right?) A simple scatter plot can reveal a curvilinear relationship.

(3) Inspection of residuals.  If you try to fit a linear model to curved data, a scatter plot of residuals (Y axis) on the predictor (X axis) will have patches of many positive residuals in the middle, but patches of negative residuals at either end (or vice versa).  This is a good sign that a linear model is not appropriate, and a polynomial may do better.

 

6. curve fitting model

https://statisticsbyjim.com/regression/curve-fitting-linear-nonlinear-regression/