x y equation determination for prediction purpose

Question

Dear all,

I need a help about to determine x-y relationship determination. I have 6 batches and I analyzed them at different days. (22 times). I try to graph x= timepoint y= measurement graph and then create the most suitable equation between them. Linear, qubic or etc... How can ı determine to most suitable equation to determine when timepoint x= 6 y=? value?

Is there anyone can help about this?

Mark_Bailey · Answer

Yes, you should not use R square or RMSE for model selection. Yes, you should either use a criterion such as AICc or use an honest assessment method like cross-validation.

Cross-validation uses two or three exclusive partitions of the data (hold out sets). The first set is used to train (fit) the model. The second set is used to validate the model selection. The optional third set is used to test the selected model. You can either designate the validation sets according to your own partition scheme or use K-fold cross-validation. You can take K-folds to the extreme and use leave one out validation.

I think that AICc is more than sufficient in your simple case of a single predictor (time).

So, yes, there are many ways to decide what is the most suitable curve for your data set. I also mentioned, and then another respondant re-iterated, that a theoretical model is usually the best when it is availble. The choice of the criterion for model selection and the selection of the best curve is up to you.

There is a reason that we have many criteria. There is a reason that JMP orders the candidates models by AICc.

nac · Answer

When ı am selecting to most suitable curve (equation) for obtained results, I try all fit options and then look their Rsquare and RMSE values. If R2 value higher and RMSE value is lower it is most suitable equation for me. Therefore ı choose Quintic curve which is highlighted with yellow color on picture. But as ı understand from your comments, you decide the most suitable equation from AIC values? Am i right?

Is there a way deciding to most suitable curve for my data set? Which model is the most suit to my results?

Can you help about it

galactus3000 · Answer

I would also think that the "physics" of the processes generating the result measurement over time would also be a factor in choosing which model is most suitable. So, if for instance the decrement possibility per unit time per unit measure of result is constant, the exponential function might apply.