Dear Mr. Niftiyev, your dependent variable varies betweem -2,5 and +2,5. Hence, it is better to employ a Tobit, Probit or Logit approaches if possible. The choice between these three approaches depends mostly on the distribution patterns of the variables.

Dear Elkhan Richard Sadik-Zada

Thank you. My dependent variables are mostly normally distributed while oil-related predictor variables are not normally distributed. Also, I hope Tobit, probit or logit are not difficult to master because I have never used them before.

Best

Ibrahim

What are the range of dependent variables?

Dear Babak Jamshidi

dependent variables range between -2.5 and +2.5

I am sorry. I made a mistake. The range of independent variables?

If the range of independent variables are wide enough, small coefficients and high significance values are consistent and explainable. Because the multiply of the obtained coefficients by the explanatory variables leads to a meaningful part of the range of the dependent variable of interest. Good luck. Babak Jamshidi

Ibrahim -

As I think Babak says, What fraction of predicted y is contributed by the parts using those coefficients?

Also, I encourage you to use graphical residual analyses. If you plot predicted y on the x-axis and estimated residuals on the y-axis, you can check model fit, as well as probably see how important heteroscedasticity might be. I like to suggest to people that if they put two or more models' results on the same scatterplot, they can make a comparison. Here you could see the impact of removing or adding an independent variable. Also, if you could use cross-validation to check for overfitting to a particular data sample, that would be helpful. A suggestion I have also previously made in such a case on ResearchGate is that if you could put together two samples, you could compare models on one scatterplot using graphical residual analysis with one sample, and then do it again for the other sample on another scatterplot. If one model is consistently better, you might have something, unless the two samples do not adequately cover what is needed for the population.

As for heteroscedasticity, I have a project on that on my profile page, including a spreadsheet tool for finding a good coefficient of heteroscedasticity for regression weights.

Best wishes - Jim

I just assumed OLS is what you needed, basically, though I encourage WLS (weighted least squares) regression instead. Note that here it would be nice if the estimated residuals (or their random factors when looking at WLS) were approximately 'normally' distributed, but data can be of any distribution, and in fact I have worked with a great deal of highly skewed data using linear regression.

However, I think Richard has a point that you should see if what you might really want might be logistic or other regression. You could check to see if such a regression would tell you what you want to know, and will it properly handle your data. I'd leave that determination to someone other than me. :-)

Thank you dear Babak Jamshidi

Dear James R Knaub

Thank you so much for the detailed suggestions and clarifications.

Best

Ibrahim

Numerically or in terms of t-ratios?

Chia-Lin Chang numerically

Dear Ibrahım Niftiyev,

Do the models you run in OLS meet the assumptions? Effective results are obtained only if the OLS estimate provides the necessary assumptions (Heteroskedasticity, autocorrelation, multicollinearity, etc.). Otherwise, you are interpreting the invalid model. This explains why your results turned out that way. Today, it is very unlikely that there will be a linear relationship between variables. So my suggestion is to try model predictions that take nonlinear structures into account.

As a theorical approach you can remove variable with small coefficients in model. But if your research has a main conseptual model, you should recheck conseptual model and variables .

Dar Tuğçe Acar

Thank you for your answer. Mainly my estimated models pass from the tests you mentioned. My main suspect is that my independent variables' range is extremely big while dependent variables only range between -2.5 and +2.5.

Best

Ibrahim

Thank you dear Shahram Rostampour

Simply multiply your dependent variable by 100 or 1000 to get coefficients that are easier to understand. For example, if you multiply by 100 your coefficients will be multiplied by 100 and your t statistics will stay the same.

Agree with John, or the other way around, i.e., divide your independents with some number that make them smaller in range. Just be careful in interpreting the result bcs you have changed the unit of measurement.

Dear Ibrahim:

Having a small coefficient is not a problem, having a statistically insignificant coefficient is more a challenge. Several suggestions made above are quite good. First, make sure your empirical model is consistent with the theoretical framework from which it is derived.

Second, make sure the classical assumptions concerning OLS are more or less satisfied.

Third, make sure you have a nice clean dataset, e.g., the dataset has sufficiently large number of useable observations.

Fourth, you can always cause the size of the estimated coefficient to be larger or smaller by changing the measurement unit of the independent variables, e.g., instead of 10,000, reduce it to 10 and make sure you inform the readers of the measurement unit. I would also be consistent and do the same to all independent variables.

If the coefficient is statistically significant and is of the expected sign, then this variable is a significant variable but has a small impact. Unless there is something in your theory which suggests that this variable should have the most important impact, then, there is absolutely nothing to worry about the coefficient being "small".

I would go on to do some additional analysis, e.g., are there simultaneity involved in the regression? Check for robustness of the estimates by dropping "insignificant" variables, etc.

Good luck with your research.

Thank you dear Francis W Ahking for your valuable comments. I will follow your recommendations. Good luck to you too.

Thank you John C Frain and Carlos Mangunsong

Dear Ibrahim,

It is not a problem.

Coefficients could be small and statistically significant in some cases.

But also consider the following:

1. Make sure you are in line with the OLS assumptions. If not, your result is not valid.

2. You can adjust your coefficients by multiplying by 10.

100 and 1000 may be too much.

3.Carry out some post test for validation of your result.

Regards

Kehinde Mary Bello thank you very much

Ibrahim -

I see that you have another question out now where they might both be about the same modeling. Is this for a finite population? I wonder if you have tried weighted least square (WLS) regression? I have a project where I have been looking at the nature and estimation of the coefficient of heteroscedasticity, and how it may be a good sign for the fit of your model when there is heteroscedasticity of the estimated residuals.

There are some examples of looking at that here:

https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity

and you can do that with your data, using this:

https://www.researchgate.net/publication/333659087_Tool_for_estimating_coefficient_of_heteroscedasticityxlsx

Cheers - Jim