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Wikipedia, defines $R^2$ or R-squared as follow:

In statistics, the coefficient of determination, denoted $R^2$ or $r^2$ and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s).

It is a statistic used in the context of statistical models whose main purpose is either the prediction of future outcomes or the testing of hypotheses, on the basis of other related information. It provides a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model.

I couldn't completely understand the above definition about $R^2$. In the first paragraph, I'm not sure how variation in the dependent variable can be predicted by independent variables. To be specific, I cannot figure out what does predicting variation of a variable mean, I know about predicting a variable but not predicting variation of a variable.

Also in the last part of the second paragraph, what does proportion of total variation of outcomes explained by model mean? For example, for $R^2= 0.9$ I think it means that %$90$ of variation of dependent variable is explained by the model. I couldn't figure out the meaning of variation being explained by a model.

Etemon
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  • The thing you quoted is an informal description of what $R^2$ is meant to compute. The actual definition of $R^2$ involves a bunch of algebra. You can find the definition(s) about 4 paragraphs later on the Wikipedia page. Does the number computed actually 'represent the proportion of variation explainable by the independent variables'? As you have observed in your "I couldn't completely..." paragraph, knowing the meanings of all the words in the description is essential. That means that you have more reading to do. – John Hughes Nov 18 '23 at 13:28
  • @JohnHughes Thanks for the advice! Yes I'm inexperienced in this subject and need to study more. – Etemon Nov 18 '23 at 19:26

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