Multiple linear regression : how to interpret the F statistic ?

[Geolien Bautistelli]

Dear Statlist,

I am quite new on Stata and I meet some issues reading outputs of my tests. I am actually doing multiple linear regression (output below ) and I am interested in interpreting the Fisher Statistic in order to determine if my model is globally significant or not. However, I don't know how to read my results : F : 32.82 and Prob > F : 0000
Can someone help me with it and tell me what are the hypothesis ?

Best regards,

Geolien,

[Marcos Almeida]

This question is deeply related to the core knowledge concerning regression analysis. It does not relate to how new we may be with the use of Stata. You shall find this information in any decent textbook of the matter. Also, in the Stata Manual, example 1 of - regress - command:

The F statistic tests the hypothesis that all coefficients excluding the constant are zero

In other words, if we have a significant p-value for the overall F test, we can state that this model (i.e,, the "package" of combined coefficients) is superior to the intercept-only model. Additionally (but for a few exceptions), we may infer that at least one predictor presents a statistically significant p-value.

That being said. in the example you shared above (please prefer to avoid snapshots, please use - dataex - or CODE delimiters, as recommended in the FAQ), there are only 43 observations, yet the model presented 9 predictors and a very high R-squared. Under such scenario, I would suspect of overfitting.

[Carlo Lazzaro]

Geolien:
I do share Marcos' opinion about the results of your regression:
As an aside, please note that the rule of thumb states that 20 observations per predictor are advised for multiple linear regression (Katz MH. Multivariable Analysis. Second Edtion. NY: Cambridge University Press, 2006: 81), even though 10 obs per predictor may sound wise enough (but take also a look at
Portnoy's suggested ratio: https://projecteuclid.org/euclid.aos/1176346793).

[Geolien Bautistelli]

Dear Marcos and Carlo,

Thank you for your answers. Marcos, I'll avoid snapshots in the future.

Kind regards,