Theoretically Based Dynamic Regression (TDR)—A New and Novel Regression Framework for Modeling Dynamic Behavior

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The submitted manuscript introduces a regression framework termed Theoretically-based Dynamic Regression (TDR) for modeling dynamic behavior in systems characterized by lag (τ) and dead-time (θ). Unlike traditional lagged-based empirical approaches, the proposed TDR approach incorporates theoretically interpretable parameters and offers a parsimonious modeling structure with fewer unknowns.

The paper is well-motivated and addresses an interesting problem in dynamic regression modeling. As demonstrated by the authors, the proposed methodology has several strengths/ advantages over other lagged-based statistical methods including Dynamic Regression (DR) and NARMAX. The empirical example of the TDR approach highlights the practical relevance of the approach, and the results support the effectiveness of TDR in capturing complex dynamic behavior.

Author Response

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Reviewer 2 Report

Comments and Suggestions for Authors

The paper proposed two theoretically-based dynamic regression as compared to the generally used lagged-based methods to model a dynamic system. The advantages of the method are their capability of catching dynamic behaviors with limited parameters, their good interpretation and performance. Overall the paper is well-written and here are some minor comments which could be considered:

• The choice of first-order and second-order TDR have not been clearly stated, could you add more details about how to select proper models.
• The performance measure r_fit is introduced and please provide an instruction about how large the measure is to consider an acceptable/ good fit when modeling the dynamic system 
• For some of the dataset, provide more clear sources if possible 
• Limitation could be further expanded to discuss under which condition the models perform not so well.

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

This work proposes a dynamic modeling approach that uses static regression modeling structures. My comments are as follows:

1. Modify line 16-17 of the abstract and include the results and conclusion.
2. Modify line 100-102 on methodology.
3. All the results and Tables 6 & 7 on weight data set should be presented in section 3.1 instead of some discussions from line 315-323 and let only the discussion of the results be in section 4.1.
4. Section 3.2 should contain only the result but line 428-433 showed some discussions of the result. The results including Tables 8-10 on distillation data set should be presented in section 3.2 and let all the discussions be moved to section 4.2.
5. Delete Table 8-10 which is reproduced from literature [29] already cited.
6. Reduce section 5: conclusion and increase your discussion on section 4.2.

Comments on the Quality of English Language

Some paragraphs need to be modified for clarity.

Author Response

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Author Response File: Author Response.pdf