Bakhita -

(Not exactly my area.  I am not familiar with your software.  By using the word "fixed" on the first line in red that you show, have you accounted for serial correlation as Pankaj notes you should?)

Your estimated coefficient standard errors should improve with larger sample sizes, but perhaps you just need a better model.  Independent variables may perform substantially differently in different combinations, but when you eliminated what appears to be your 'worst' independent variable,  I don't think you should really expect much improvement, nor much degradation either.

If you are interested in performance, you can use graphical residual analyses to compare fits of various models, which you might consider based on subject matter knowledge.  Test data (i.e., not used in model selection or estimation of regression coefficients) can be used to avoid overfitting. 

You might be interested in the estimated variance of the prediction error for each prediction, which will vary due to heteroscedasticity.  These estimated variances use estimated sigmas which are impacted by bias, so each may be a good overall indicator of accuracy.  From these estimated variances of prediction errors, you might be interested in prediction intervals on predicted y values, rather than confidence intervals on regression coefficients.  But don't forget autocorrelation and heteroscedasticity.

Here you might just want to compare model performances by use of graphical residual analyses and test data to find the best model that you can find, and have an idea as to the fit. 

Cheers - Jim

In panel data, there should be autocorrelation. In case autocorrelation the data does not follow prerequisite assumptions of normal regression model, so normal regression model not suitable for the data. That's why your fitted model not provide good results. First check the PACF and ACF your data and according to ACF and PACF fit model.

Bakhita -

(Not exactly my area.  I am not familiar with your software.  By using the word "fixed" on the first line in red that you show, have you accounted for serial correlation as Pankaj notes you should?)

Your estimated coefficient standard errors should improve with larger sample sizes, but perhaps you just need a better model.  Independent variables may perform substantially differently in different combinations, but when you eliminated what appears to be your 'worst' independent variable,  I don't think you should really expect much improvement, nor much degradation either.

If you are interested in performance, you can use graphical residual analyses to compare fits of various models, which you might consider based on subject matter knowledge.  Test data (i.e., not used in model selection or estimation of regression coefficients) can be used to avoid overfitting. 

You might be interested in the estimated variance of the prediction error for each prediction, which will vary due to heteroscedasticity.  These estimated variances use estimated sigmas which are impacted by bias, so each may be a good overall indicator of accuracy.  From these estimated variances of prediction errors, you might be interested in prediction intervals on predicted y values, rather than confidence intervals on regression coefficients.  But don't forget autocorrelation and heteroscedasticity.

Here you might just want to compare model performances by use of graphical residual analyses and test data to find the best model that you can find, and have an idea as to the fit. 

Cheers - Jim

There is nothing wrong with the "model." What is problematic is how the model is applied. Here, you pre-specified the model (pre-select) then force the data to fit the model. The result shows pValue = 0.43771 which tells you it does not work; this model is not appropriate for this data.

The starting point should be: (i) what is the nature of the data for each variable? If putting them together, what is the appropriate model? The data should lead you to model selection. By having a prejudice or bias in favor of a certain model and force it on the data, regardless how the data behave- - -distribution types, etc., you will end up with results as shown.

SUGGESTION: (i) verify data distribution, (ii) model selection according to data distribution, (iii) with the right distribution matching the model, hypothesis testing comes as a logical process in the analytical process.

For model selection, see links below:

https://pdfs.semanticscholar.org/2de7/25762bb25ac0de397032a03506f17837c850.pdf

https://helda.helsinki.fi/bitstream/handle/10138/161437/modelsel.pdf?sequence=1&isAllowed=y

https://www.stat.berkeley.edu/~binyu/summer08/Hurvich.AICc.pdf

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.127.1018&rep=rep1&type=pdf

I think your data are having some issues. As mentioned by Pankaj and James, your model may have correlation issue. F value of your model is very low, please check for relevant independent variables.

Have you run the Hausman Test which suggests you whether to employee Fixed Effect or Random Effect. model I also support the above statement mentioned by Muhammad Ishaq.

Best of luck.

This data might have a problem of Multicollinearity, check the correlation among the used variables and try to remove the Multicollinearity if there exist any. And also try building a model by considering different combination of variables.

If im reading this right, you have a large N of cross-sections and small number (T?) of time points. Cross-sections dominate - coefficients are largely differences between cross sections.

You can follow others suggestions, especially correlation among IVs , but looks to me like there are no net effects of X on Y.