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I was researching about the line of best fit and came upon this article that talked about the regression line. In the beginning, everything seemed similar to the best fit line, but then I came upon this :

enter image description here

And I can't understand why to go through this when you can simply use: y=mx+b. Don't they give the same result?

IB MR
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  • Is there any difference between the regression line and the line of best fit at all ? If not (what I think) the formula should be equivalent to the other. – Peter Aug 15 '19 at 08:30
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    "you can simply use $y = mx + b$" The purpose of linear regression is to figure out the best values of $m$ and $b$ to use when fitting a line $y = mx + b$ to data. – littleO Aug 15 '19 at 08:40

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In order to use $y=mx+b$, you would need to find out the values of $m$ and $b$. And from the least squares method, the value of $b$ is obtained from the equation you wrote. So they are part of the same method.

Matti P.
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  • So there is no reason to use the more complex formula? – IB MR Aug 15 '19 at 08:31
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    More complex than what ? – Peter Aug 15 '19 at 08:33
  • @Peter than y=mx+b – IB MR Aug 15 '19 at 08:34
  • @IBMR What values of $m$ and $b$ do you propose to use? – littleO Aug 15 '19 at 08:35
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    I guess you didn't really understand the article you posted. The equation $y=mx+b$ is the final form of the approximant, but you obviously need to figure out what the values of $m$ and $b$ are. The "complex" equation is required to do so. Here is another question, talking about a similar question: https://math.stackexchange.com/questions/3076868/linear-regression-computation-as-y-ax/3076898#3076898 – Matti P. Aug 15 '19 at 08:35
  • Oh so it's the derivation of the y=mx+b. I see now, thanks – IB MR Aug 15 '19 at 08:37