the multiple linear regression formular "Y=b+bX +bX +␣+bX +εi is using the natural logarithm for Y and X. do you know why? i think i’ve read the explanation somewhere, but i don’t remember where in the book they put the explanation. appreciate if you can explain.
You can’t model exponential growth with OLS regression. Using the log makes it linear.
To be clear: you use log(Y) (_ but not _ log(X)) to make it linear when the growth is exponential (Y = k^X, so log(Y) = log(k) × X).
Using log(Y) _ and _ log(X) is the approach when Y = X^k; then log(Y) = k × log(X), which is linear.