What is the significance of orthogonality in regression












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Can somebody please explain intuitively why the variables need to be orthogonal to each other? Does orthogonality imply independence? When the variables are independent then we get an estimate using the least squares optimization. But, when they are not orthogonal, we cannot regress the variables. Therefore, my questions are:



1) what is the significance of orthogonality, why is it needed



2) how to know the variables are orthogonal and how to make them orthogonal if not?



3) does orthogonal imply mutually independence?



Thank you









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    0












    $begingroup$


    Can somebody please explain intuitively why the variables need to be orthogonal to each other? Does orthogonality imply independence? When the variables are independent then we get an estimate using the least squares optimization. But, when they are not orthogonal, we cannot regress the variables. Therefore, my questions are:



    1) what is the significance of orthogonality, why is it needed



    2) how to know the variables are orthogonal and how to make them orthogonal if not?



    3) does orthogonal imply mutually independence?



    Thank you









    share









    $endgroup$















      0












      0








      0





      $begingroup$


      Can somebody please explain intuitively why the variables need to be orthogonal to each other? Does orthogonality imply independence? When the variables are independent then we get an estimate using the least squares optimization. But, when they are not orthogonal, we cannot regress the variables. Therefore, my questions are:



      1) what is the significance of orthogonality, why is it needed



      2) how to know the variables are orthogonal and how to make them orthogonal if not?



      3) does orthogonal imply mutually independence?



      Thank you









      share









      $endgroup$




      Can somebody please explain intuitively why the variables need to be orthogonal to each other? Does orthogonality imply independence? When the variables are independent then we get an estimate using the least squares optimization. But, when they are not orthogonal, we cannot regress the variables. Therefore, my questions are:



      1) what is the significance of orthogonality, why is it needed



      2) how to know the variables are orthogonal and how to make them orthogonal if not?



      3) does orthogonal imply mutually independence?



      Thank you







      machine-learning terminology





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      asked 6 mins ago









      Srishti MSrishti M

      1996




      1996






















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