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Suppose you have a set of data $y_i$ and the corresponding linearized data $f_i$ obtained through linear regression.

Set: $$(R')^2=\frac{\sum_i (f_i-\bar{f})^2}{\sum_i (y_i-\bar{y})^2},$$ that is a fraction with the same denominator as the usual regression coefficient $R^2$ but at the numerator you put the average $\bar{f}=\sum_i f_i/n$ of the linearized data instead of the average $\bar{y}=\sum_i y_i/n$ of the real data.

Has this coefficient $(R')^2$ any significance? How it compares to $R^2$?

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  • $\begingroup$ the mean of the linearized data is the same as the mean of the real data (so long as your model has an intercept). $\endgroup$
    – John Madden
    Commented Jan 12 at 19:25
  • $\begingroup$ Can you please provide an explanatory link or a short explanation about why? $\endgroup$
    – user404935
    Commented Jan 12 at 19:39
  • $\begingroup$ for sure stats.stackexchange.com/questions/469212/… $\endgroup$
    – John Madden
    Commented Jan 12 at 19:41
  • $\begingroup$ Great! Many thanks! $\endgroup$
    – user404935
    Commented Jan 12 at 19:45

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