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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 ... t-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?.

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.