How is the regression equation calculated in multiple linear regression ?

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I understand how we calculate the Coefficeint and Intercept in the simple linear regression using least squares method and Gradient descent , now I am trying to understand how does multiple linear regression work , but the main issue is everywhere I looked the implementation is very abstracted using ML libraries like scikitlearn , I mean how do we even get this equation ?

Y=B + M1*X1 + M2*X2...MnXn

I am looking for the geometric meaning of the above equation used in multiple linear regression.

Any help is appreciated.

What I have tried:

I tried looking for resources online but the detailed are abstracted.

Posted 8-Mar-21 1:49am

deepeshdm3434

Updated 8-Mar-21 7:38am

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Richard MacCutchan 8-Mar-21 8:06am

I think the question is about mathematics, rather than programming.

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CPallini · Answer 1 · 2021-03-08T07:20:00

Solution 1

Quote:
Y=B + M1*X1 + M2*X2...MnXn

Defines a hyperplane (see, for instance Hyperplane - Wikipedia[^]).

In two dimensions you have the usual straight line. In three dimensions you have the usual plane. When you have more than three dimensions, then, well..., you need a bit of imagination.

Posted 8-Mar-21 7:20am

CPallini

Patrice T · Answer 2 · 2021-03-08T07:38:00

Solution 2

Quote:
How is the regression equation calculated in multiple linear regression ?

Looks like you need to study the subject.
Linear regression - Wikipedia[^]
Excel analysis toolpack Have a toll about it:
Analysis ToolPak in Excel - Easy Excel Tutorial[^]

Posted 8-Mar-21 7:38am

Patrice T