Dear all
I have an query that if we are taking independent variables as GDP, Per capita income for regression then it is wise to use their log values instead of full number as values of unstandardized co-efficients appears very low. Guide me in this regard.
Kind regards
Sheetal
Check which one gives a linear relationship, since it is the assumption for regression (unless you're using non-linear regression, but in this case the question is pointless [except in case of numerical instabilities, may be], just write the model with the variable you prefer and fit it.
When the value of the X and Y are disproportionate, log is used. For instance, if you want to run regression for the relationship between savings rate, i.e. 0.30 or 30% as Y (dependent variable) and GDP of 30,000 as X (independent) to test whether "GDP explains the savings rate"? Without taking the log of the GDP, the regression run will shows there is no relationship, but if the GDP amount is log first, you can pick up some signal. See attached figures for illustration.
The purpose of LOG is scaling the values of the data so that it is more manageable and sometimes-----in your parametric case, log the values first before regressing, allows you to magnified the relationship between X and Y that would have not been otherwise be not be noticeable due to disproportionate scale between X and Y.
In time series analysis, log is sometimes taken in order to linearise any trend in the data.
@ Paul: incommensurability is not a good reason to take log. You can always make X and Y commensurate by centering and scaling, for instance in your example using X/1000 or X/10000 (changing the unit). Obviously, in your example, the value of the coefficient appears to be 0 because of insufficient significant digits.
Note also that the p-value are the same in your two models. If there is no relation, either X or log X will not make it one appear, and the apparent higher value of the coefficient is meaningless, it's just a scale (unit) effect.
Taking log if the Y and X relation is linear will make it non-linear, and vice versa, so transformation effects should be checked. Scaling has no such drawback. So, to resolve incommensurability only, you'd better use scaling.
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