In #datamining, we are bored by linear regression. It does not work very
well and I have personally never seen a qqplot that was strictly on a line,
anyway. But besides this practical approach, linear regression (still very
popular in social science) seems to have a strong theoretical foundation in the
central limit theorem. But here comes an argument derived from Hegel's Logic,
why linear regression has no existence at all:
Hegel distinguishes between "bad" infinity and real infinity. Bad infinity is the result of infinite progress. Take 2:7 as an example. If you want to solve this division, you will end up with 0.285714285714... and so on (infinite). Or think about the rock, paper, scissor game: You want to take the good old rock, but then you think, your opponent might think that you want to take rock and therefore will choose paper. So you want to choose scissor, but then you think, your opponent knows that you wanted to take rock but he realized that you had realized that he is going to take paper and therefore you would take scissor, so he will take rock and you should take paper, and so on.
Real infinity in contrast, is limited. That sounds like a contradiction, but - well it is dialectic. Think about a circle within another circle.
If the size of the orange circle can change arbitrary, how many possibilities are there for the size of the blue space? Infinite! Nevertheless, the blue space is limited by the two circles. Real infinity is a relation of different quanta. Otherwise, it would be everything (“absolutes Sein”) which is the same as nothing (“absolutes Nichts”). But everything that really is (the existence or “Dasein”) is not nothing but is becoming (“Werden”) and disappearing (“Verschwinden”).
This is true for mathematics, as well. The right answer to the problem of dividing 2 by 7 is 2/7 (as fraction). As a relation, it has no deficit. You can add 5/7 and you will get exactly 1.
It is obvious that linear regression is always bad infinity. You can always move one further on the x-axis to find another y and there is no relation, no limit.
The alternative would be a non-linear regression. The function of a linear regression is
y = a + bx + e.
y is determined by this function, a, b and e are constants. But x is a pure quantity. It can be anything and therefore drives the whole function to bad infinity. But if we take
y = a + bx² + e,
then x has a relation: x is the unity and 2 is quantity. Therefore, x is a pure quality. As a consequence, only functions which have an x to be to the power of n>1 have an existence. q.e.d.
Hegel distinguishes between "bad" infinity and real infinity. Bad infinity is the result of infinite progress. Take 2:7 as an example. If you want to solve this division, you will end up with 0.285714285714... and so on (infinite). Or think about the rock, paper, scissor game: You want to take the good old rock, but then you think, your opponent might think that you want to take rock and therefore will choose paper. So you want to choose scissor, but then you think, your opponent knows that you wanted to take rock but he realized that you had realized that he is going to take paper and therefore you would take scissor, so he will take rock and you should take paper, and so on.
Real infinity in contrast, is limited. That sounds like a contradiction, but - well it is dialectic. Think about a circle within another circle.
If the size of the orange circle can change arbitrary, how many possibilities are there for the size of the blue space? Infinite! Nevertheless, the blue space is limited by the two circles. Real infinity is a relation of different quanta. Otherwise, it would be everything (“absolutes Sein”) which is the same as nothing (“absolutes Nichts”). But everything that really is (the existence or “Dasein”) is not nothing but is becoming (“Werden”) and disappearing (“Verschwinden”).
This is true for mathematics, as well. The right answer to the problem of dividing 2 by 7 is 2/7 (as fraction). As a relation, it has no deficit. You can add 5/7 and you will get exactly 1.
It is obvious that linear regression is always bad infinity. You can always move one further on the x-axis to find another y and there is no relation, no limit.
The alternative would be a non-linear regression. The function of a linear regression is
y = a + bx + e.
y is determined by this function, a, b and e are constants. But x is a pure quantity. It can be anything and therefore drives the whole function to bad infinity. But if we take
y = a + bx² + e,
then x has a relation: x is the unity and 2 is quantity. Therefore, x is a pure quality. As a consequence, only functions which have an x to be to the power of n>1 have an existence. q.e.d.
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