R2 interpretation

Econometrics questions and discussions

R2 interpretation

Unread postby jack » Mon Jun 11, 2018 3:18 am

Hi dear Tom.

I have a question about interpretation of R2.

The Economist has built a statistical model to identify what makes a country good at football: "What makes a country good at football?".
https://www.economist.com/international/2018/06/09/what-makes-a-country-good-at-football

In a apart of the article, it says:

Our model explains 40% of the variance in average goal difference for these teams.



Is it the interpretation of R2 in this regression: regression of average goal (per a match) of teams on GDP per capita, football’s popularity ........?

Or

Is it the interpretation of R2 in this regression: regression of average goal difference (per a match) of teams with respect to median team on GDP per capita, football’s popularity........?


I am sorry for asking such a simple question but I am really confused about it.

I would be really grateful if you could possibly guide me about it.

What about the following interpretation of R2:

suppose we regress the GDP per capita of countries on, for example, their inflation rate. suppose the R2 of this model is 50 %.

Can one say: 50 % of the difference between GDP per capita of countries is due to the difference between their inflation rate?.
Last edited by jack on Mon Jun 11, 2018 3:25 pm, edited 1 time in total.
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Re: R2 interpretation

Unread postby TomDoan » Mon Jun 11, 2018 9:52 am

Clearly, most of the work in this is behind the scenes, because they need to convert raw football scores into "average goal differential vs a median team". (A Germany vs Brazil game doesn't directly tell much about how either would do against a "median" team). But treating that generated number as data, what they're saying is the regression explains 40% of the variation among countries in the "average goal differential vs median team", which isn't bad for a cross section regression.

jack wrote:What about the following interpretation of R2:

suppose we regress the GDP per capita of countries on, for example, their inflation rate. suppose the R2 of this model is 50 %.

Can one say: 50 % of the difference between GDP per capita of countries is due to the difference between their inflation rate?.


No. That's the famous "correlation vs causation" issue. All the R^2 measures is correlation (association). When you have just two variables, the R^2 is the same both ways, so you would get the same 50% in a hypothetical regression of inflation rate on GDP per capita.
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