I conducted a multiple linear regression using gretl for my exploratory research. The data was from published reports from 2013 to 2021, as these were the periods where all the yearly data was recorded. The results show that two of my variables are significant at 10% and have an r-square value of 0.664428, but the overall model fit comes to F(3,5) = 3.299978 and p-value (F) = 0.115750. So, can I go forward with this result or not and how can I justify this result?
You would not interpret any of the individual variable significance tests when you find that your omnibus F test is not statistically significant. The reason for a non-significant result despite large R^2 value is likely your very small sample size.
Christian Geiser Thank you for your observation. I do have one more doubt, The data was taken from published government reports for a period from 2013 to 2021, as these were the periods where all the yearly data was recorded for the dependent and independent variables. Still, can we explain this result or do we neglect the result
I think you should see a fundamental concern in the view of @Jochem Wilhelm. However, when your sample size decreases, the power of the test also suffers. Your interpretation, since you are only exploring should be limited to the limitation of sample size in the study.
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