In the case of Linear Regression models, some data has residual terms influenced by a predictor term (heteroscedasticity). Taking a case where the residual increases with increase in predictor value, transforming the data using a concave function like log Y might help.

But how does this impact other aspects of the model? Is there a disadvantage? Is a weighted least squares fit better in this case?

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Hi Hari,

Fitting the model $\log{Y} = \beta X + \epsilon$ doesn't have a disadvantage per se, but of course the way you interpret $\beta$ changes. In this case, a one unit increase in $X$ leads to a $(e^{\beta}-1) \times 100 \%$ increase/ decrease in Y rather than a $\beta$ change in $Y$.

Unfortunately I don't know enough about weighted least squares to help with your last question. Hopefully somebody else can!

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Thanks for the reply.

Hari
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