I'm doing a linear regression assignment using a variable transformation using R. and I have several questions.
- What is the criteria of choosing which type of variable transformation? We've learnt "Y~X", "logY~X", "logY~logX". Out of three, how can I choose the model?
1-1. Should I look at the plot line? It is as below (Company 1 and 2). I drew the line using loess. If so, I think Company 1 should have Y~X (without transformation) because plot itself looks quite linear; Company 2 should have logY~BlogX with negative coefficient B.
Company 1
Company 2
1-2. Can highest adjusted R squared be a criteria? Someone says the dependent variable should be same, which means it cannot be used as a criteria because Y and logY are not same.
When I use logY~logX model, should I log the intercept? For example, the model would be like logY = (intercept) + BlogX + e. If so, should I log the intercept when I write the final model equation? Or is it already logged?
When I transform the model with a dummy variable and variable including 0, what can I do? For example, my model should be logY = Intercept + BlogX1 + X2 (dummy) + X3 (including zeros). Can I just leave X2 and X3 as it is, without logging?
3-1. Then the same question with 2. Should I log the result coefficients of X2 and X3?
I'm so lost..... Thank you so so much!!!! Have wonderful days! XD
