Is the statement "Pearson’s r is a measure of goodness of fit to an affine function" literally true? Why or why not?
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Is this an assignment? – Nick Cox Aug 11 '23 at 14:37
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Doesn't https://stats.stackexchange.com/questions/180777 answer this? If not, why not? – whuber Aug 11 '23 at 16:59
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@NickCox No. I'm not a student (see my other questions/answers). – BigMistake Aug 11 '23 at 19:36
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@whuber I am specifically wondering about the word "affine," as I am not too familiar with it. For example, there might be differences in the meaning between affine and linear (e.g. transformations perhaps). – BigMistake Aug 11 '23 at 19:37
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1There might be exotic mathematical spaces where this fails (I don’t know of any), but, at least usually, an affine function is a linear function followed by a shift, something like $f(x) = L(x) + s$ or $y=ax+b$. In other words, it is the human definition of linear as meaning that the graph looks like a line (instead of the mathematical definition of a linear transformation as $T(ax+by) =aT(x)+bT(y)$). – Dave Aug 11 '23 at 19:54
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For a definition that has appeared here on CV, please search our site for "affine." I offer one at https://stats.stackexchange.com/a/161382/919. Affine transformations are closely related to linear ones, btw: the affine transformation $x\to Ax+b$ ($x$ and $b$ are vectors and $A$ is a matrix) can be written as $$\pmatrix{A&b\0&1}\pmatrix{x\1},$$ which is a linear transformation of the vector $x$ to which a $1$ has been appended. – whuber Aug 11 '23 at 22:27