Here below 2 questions.

A typical linear model assumption says that the error terms are normal, which implies that the conditional distributions of Y given X=x are normal. The unconditional (marginal) distribution of Y need not be normal, and it is not relevant to check for normality of Y. Residual diagnostics are usually used to check whether the assumption of normality holds (at least approximately) for the error terms. That, along with other assumptions, is what matters for correct inference using the usual techniques.

While fitting regression, I know that when the response-variable (Y) is right skewed and Y>=0, using log(Y) or log(Y+c) for a small constant c such that min(Y_i + c) > 0 can help. Sometimes, in econometrics, transformations are of interest such as the log-log model for elasticity or such as log (p_t/p_t-1) approximates the rate of return.

However, I really don’t like (log) transformation or any other box-cox transformations for many reasons, I much more prefer to work with raw data without transformation. Of course, if the skeweness is due to the presence of outliers, we can use robust estimation.

1) In my opinion, for inference (i.e. calculate the confidence intervals of Beta's coefficients) everything is fine as long as the residuals look fine in general, even if the response-variable (Y) is highly skewed. Do you agree ?

2) Now, if my goal with my regression model is not inference but prediction/forecasting. Is it a problem for prediction/forecasting if "Y" is (highly) skewed ?


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