Is there any way to know whether data follows normal distribution by taking a look at regression coefficient?
can we establish any relation between these two terms... or such relationship is already in common practice for ease of data analysis...?
I don't really understand what you are asking. Do you want people to recommend tests for normality?
Dear Sandeep,
Normality is a property of a single data set.
Regression coefficients can be calculated between two related data sets.
The Pearson correlation regression coefficient should only be quoted when the data sets meet the assumption of this model. It is possible to use Pearson correlation with non-normal data in certain circumstances. I would recommend a Koenker test for homoscedasticity before calculating Pearson correlation.
No, you can't see whether variables are normally distributed by looking at a regression coefficient alone.
NORMALITY ASSUMPTION
It is assumed in multiple regression that the residuals (predicted minus observed values) are distributed normally (i.e., follow the normal distribution). Again, even though most tests (specifically the F-test) are quite robust with regard to violations of this assumption, it is always a good idea, before drawing final conclusions, to review the distributions of the major variables of interest. You can produce histograms for the residuals as well as normal probability plots, in order to inspect the distribution of the residual values.
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