Different length of predictors to train a regression model

I want to train a Gaussian regression model to predict the wind speed based on fan RPM.

I experimentally tested different d(RPM)/dt inputs and measured the wind speed for each input.

In other words the inputs are:

RPM1= 200:10:500;

RPM2=200:20:500;

RPM3=200:30:500;

and three velocity vectors (V1,V2 and V3) are measured.

Now I want to train a universal model with these predictors: RPM1, d(RPM1)/dt, d(RPM2)/dt and d(RPM3)/dt. The reponse value would be V1. But the length of the predicotrs are different. Also, they ( predictors) have different length campared to response (V1).

Question1)

What is the proper way to train the model? Examples would be exteremly helpful

Question 2)

In general, do I need to introduce d(RPM)/dt as a predictor or the algorithm is "smart" enough to figure that out? In other words, can I just feed the model with RPM1, RPM2 and RPM3?

Thanks

[harsha001]

for your question1 it is not clear why you are generating RPM1 like that?

a) Are d(RPM1)/dt, d(RPM2)/dt ... constant? If yes, why don't you generate RPM1 as

0: dRPM1dt : (nSamples-1)*dRPM1dt

where dRPM1dt is the constant rate, and you will have nSamples for each vector

b) if d(RPM1)/dt are not constant, you will need to interpolate all vectors (predictor and co-variate to same "timepoints")

Could you clarify your variables?

2) Yes, you need a column for each predictor.

[sarah Abdellahi]

Thanks for your time, I am really confused about your response tho!

a) I want my RPM to go up from 200 to 500 with different rates. What you suggested makes the length of the input similar, but the maximum RPM changes. Please look at this graph. The top one is my input RPMs, the second one is what you suggest. Am I missing something?

About clarifying the variables, its simply the effects of increments in RPM on the wind speed. If I gradually increase the RPM, the wind velocity changes in a different way compared to the case where I increase the RPM suddenly (within the same RPM range).

Thanks

[harsha001]

I think you need to clarify the regression model.

This means not a verbal description like wind speed, but an unambiguous mathematical definition of what you are measuring/trying to fit? Where are your velocity vectors coming from? In other words, in your plots, what is your x-axis??

1. If the variables increase at different time-dependent rates, AND run for the same time, then you will reach different endpoints.
2. If you want the speed to saturate at 500, just pad your vectors with enough number of 500s at the end.

A regression model needs same length of predictors and co-variates (or put NaN where missing). This means everything is sampled at the same timepoints (or your equivalent index array) such that for index i=1 to N, your co-variate Y is modelled as a function F of the predictors X1,...,Xm:

Y(i) = F( X1(i), X2(i), .... , Xm(i) )

What are your Y and X's?

Example:

a) You want to fit 3 functions:

V1[time] = F1( RPM1[time], d(RPM1)/dt [time] )

and similarly for V2 and V3

OR

b)

V1[time] = F( RPM1[time], RPM2[time], ... ,d(RPM1)/dt [time], d(RPM2)/dt [time] )

In which case clarify these vectors as a function of time, making sure you use the same timepoints /time range

[sarah Abdellahi]

Please move your comment to answer so I can accept it.