How to write an equation where both independent variables and dependent variables are log transformed in a multiple regression?How to write the multiple regression model when both the dependent variable and independent variables are log-transformed?I know that without any log transformation the linear regression model would be written as enter image description here y = β 0 + β 1 ( x 1 ) + β 2 ( x 2 ) + …But now I have transformed both my dependent variables and independent variable with log. So is correct to write as enter image description here log ⁡ ( y ) = β 0 + β 1 ⋅ log ⁡ ( x 1 ) + β 2 ⋅ log ⁡ ( x 2 ) + …Or since I am transforming both sides of question so can I write it as enter image description here ln ⁡ ( y ) = β 0 + β 1 ( x 1 ) + β 2 ( x 2 ) + …

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How to write an equation where both independent variables and dependent variables are log transformed in a multiple regression?How to write the multiple regression model when both the dependent variable and independent variables are log-transformed?I know that without any log transformation the linear regression model would be written as enter image description here  y  =      β    0    +      β    1    (      x    1    )  +      β    2    (      x    2    )  +  …But now I have transformed both my dependent variables and independent variable with log. So is correct to write as enter image description here   log  ⁡  (  y  )  =      β    0    +      β    1    ⋅  log  ⁡  (      x    1    )  +      β    2    ⋅  log  ⁡  (      x    2    )  +  …Or since I am transforming both sides of question so can I write it as enter image description here  ln  ⁡  (  y  )  =      β    0    +      β    1    (      x    1    )  +      β    2    (      x    2    )  +  …

Reagan Tanner · Accepted Answer

I am afraid that all your transformed forms are false.Starting from  y  =      β    0    +      β    1    (      x    1    )  +      β    2    (      x    2    )  +  .  .  .you can write :  ln  ⁡  (  y  )  =  ln  ⁡            (            β    0    +      β    1    (      x    1    )  +      β    2    (      x    2    )  +  .  .  .            )      This is not equivalent to       β    0    +      β    1    (  ln  ⁡  (      x    1    )  )  +      β    2    (  ln  ⁡  (      x    2    )  )  +  .  .  .Also you can change of variables :      X    1    =      e                  x        1                ;        X    2    =      e                  x        2                ,  .  .  .  y  =      β    0    +      β    1    ln  ⁡  (      X    1    )  +      β    2    ln  ⁡  (      X    2    )  +  .  .  .And with the change of :  Y  =      e    y    ln  ⁡  (  Y  )  =      β    0    +      β    1    ln  ⁡  (      X    1    )  +      β    2    ln  ⁡  (      X    2    )  +  .  .  .Sorry if I misunderstood your question.

How to write the multiple regression model when both the dependent variable and independent variabls

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