If my model pass all the assumptions test for Multiple Linear Regression (MLR) except autocorrelation test is not met and there is a negative autocorrelation, should my model pass all the assumptions test? or I should fix the autocorrelation?
If I want to fix it, what should I do? Could you please help me and explain it to me.
Thanks,
Mansour
Obviously, not all assumptions need to be pass.
But pay attention to one important point.
Calculate the Multicollinearity (VIF) for each of the X's. Then remove any X's with a VIF > 5 from the model and then re-fit the MLR.
Multiple linear regression - https://www.investopedia.com/terms/l/linearrelationship.asp
Maybe you can alernatively consider the recursive least squares algorithm (RLS). RLS is the recursive application of the well-known least squares (LS) regression algorithm, so that each new data point is taken in account to modify (correct) a previous estimate of the parameters from some linear (or linearized) correlation thought to model the observed system. The method allows for the dynamical application of LS to time series acquired in real-time. As with LS, there may be several correlation equations with the corresponding set of dependent (observed) variables. For RLS with forgetting factor (RLS-FF), acquired data is weighted according to its age, with increased weight given to the most recent data.
Years ago, while investigating adaptive control and energetic optimization of aerobic fermenters, I have applied the RLS-FF algorithm to estimate the parameters from the KLa correlation, used to predict the O2 gas-liquid mass-transfer, hence giving increased weight to most recent data. Estimates were improved by imposing sinusoidal disturbance to air flow and agitation speed (manipulated variables). The power dissipated by agitation was accessed by a torque meter (pilot plant). The proposed (adaptive) control algorithm compared favourably with PID. Simulations assessed the effect of numerically generated white Gaussian noise (2-sigma truncated) and of first order delay. This investigation was reported at (MSc Thesis):
Thesis Controlo do Oxigénio Dissolvido em Fermentadores para Minimi...
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