Similar regression but different R^2

[quoctruongphan]

Hello,
I am running two equivalent model for double check. All coefficients are perfect match, but the R^2 is different between two models.
For model 1:
MDR(t) - MDR(t-1) = Beta*X(t-1) - Gamma*MDR(t-1)

For model 2: (little transformation from model 1, by moving MDR(t-1) from LHS t RHS)
MDR(t) = Beta*X(t-1) + (1-Gamma)*MDR(t-1)

In which: X present set of relevant independent var, in eviews files, they are: ebit_ta, mtb, ln_ta, rd_ta, and rd_dum.

Looking in eviews files for eq03 (model 1) and eq04 (model 2). You can see all result are perfectly equal. However, the R^2 of 2 model are greatly different, 0.56 and 0.09
Therefore, I would like to ask how could this happen? What is the reason for this different?

Thank you for looking my question

[quoctruongphan]

Hello, I move this topic up hoping that someone can help me with this problem

[EViews Glenn]

The R2 is respect to the variable on the LHS of the equation, which is different in your two examples.

[quoctruongphan]

The R2 is respect to the variable on the LHS of the equation, which is different in your two examples.

Thank you for your answer, still I am not very clear about this. Can you explain in detail?
Many thanks

[EViews Gareth]

R^2 is a statistic based, in part, on the values of the dependent variable. Your two equations have very different dependent variables, in completely different scales. It is not surprising that R^2 is different.

I guess the question is - why would you expect them to not be different? Do you expect the residuals to be identical too?

[quoctruongphan]

R^2 is a statistic based, in part, on the values of the dependent variable. Your two equations have very different dependent variables, in completely different scales. It is not surprising that R^2 is different.

I guess the question is - why would you expect them to not be different? Do you expect the residuals to be identical too?

Thank you for your reply
I understand that two equations have different value of dependent variables. To the basic form:
Model 01: Y = B1*X1 + B2*X2 + ... + e
Model 02: Y' = B'1*X1 + B'2*X2 + ... + e

In fact, when I run the regression for two models, the Beta between two models are identical, so I expect the R^2 between two models should be identical too, or at the least not too much different, say 0.56 and 0.52 would be acceptable. However, we all see that the R^2 between two models different greatly (0.56 and 0.09). This makes me confused since the different in R^2 could then lead to different conclusion that model with R^2(0.56) is better than model with R^2(0.09) - although in mathematics, two equations is the same.

For residual, I do not expect them to be identical since we have different value of dependent variables in two models. Initially, I more expect SSE between two models have approximately ratio to SST, which is SSE/SST (model 1) ~ approximately to SSE/SST (model 2).

If there is any wrong in my explanation and statement, hope you can help me.


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Today, I re-run the two models in Excel - Data Analysis Tool - Regression, and there is another problem, same coefficients but different result of R^2 (between Eviews & Excel)
- For model in Eviews with R^2 = 0.09, in Excel, the result is similar 0.09
- For model is Eviews with R^2 = 0.56, in Excel, the result is 0.86 ??

Since the pool regression does not included Fixed Effect or Random Effect, so OLS method can be applied. Then using Regression tool in Excel give no problem at all.
Maybe Eviews and Excel use different method (in term of programming) but the shift from 0.56 in Eviews to 0.86 in Excel is a big different.

What is the problem for this issue?

I upload the Excel files:
- Sheet 01: It is the raw data (similar in data in Eviews) and data is calculated to be used for regression in Excel
- Sheet 02: It is result of eq03 and eq04 of Eviews file
- Sheet 03: Result of two models using regression analysis tool in Excel - Here you can see one R^2 is 0.09 and other R^2 is 0.86

I hope if you could explain this too