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Hi Stack Exchangers,

Reaching out for clarification on two different ways to derive B0 for a best fit line using OLS. Are they related?

  • From MIT Notes, B1 is defined as the minimum sum of squared residuals (sum of X and Y from their respective means as a ratio to the spread of X from the mean_
  • From Khan Academy, B1 is defined as the R-weighted ratio of Sx and Sy

My hunch is saying that Khan's formula is only appropriate for pairs data (single X variable), while the MIT formula applies to multiple X variables.

Any clarification on the relationship or difference between these two formulas appreciated.

Thank you in advance, Lenn

MIT Reference

MIT Formula

Khan Reference Khan Notes

Lennard Ong
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  • Where you say "two different ways to derive B0 for a best fit" --- did you mean "B1" there? – Glen_b Aug 12 '22 at 04:48
  • It would be helpful to define the notation of the Khan academy more thoroughly. But the MIT formula is only for simple regression (with a constant), for multiple X you get the matrix algebra formula $(X'X)^{-1}X'y$ for the coefficient vector. – Christoph Hanck Aug 12 '22 at 09:53
  • It is incorrect to characterize the Khan Academy statement as a "definition:" it is a formula resulting from a calculation. We have so many threads on this subject that it's a challenge to find a specific one! Try this search. – whuber Aug 12 '22 at 13:40

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