A -ve beta would imply that (a) the corresponding independent variable X is -vely correlated with the Y variable, (b) the Y variable, on average, will reduce by an amount equal to the beta value for a unit change in X. If this beta value is not "statistically" significant, say at 0.05 level of significance, then one interpretation would be that Y is not 'statistically' dependent on that X. Another interpretation could be that Y is known to depend on X but the study design, used to generate the data, does not have sufficient power to detect that dependence.   

Thank you very much for your comments  Mr. Subash

Rohanaraj -

If you are looking at multiple linear regression with continuous data, one of the best places to start would be to look at various scatterplots. (You may even have to challenge your linearity assumptions.)

If you have regression coefficients (betas) that are estimated to be negative in the multiple linear regression, did you expect them to be positive? That is, if used in a simple linear regression (one regressor), would the regression coefficient have been positive, but now used in a multiple regression, the estimated beta (b) changed signs? If so, then I think that might often be an indication that interactions among your regressors are such that you may do better without using all of them. There are various complications that can occur, such as collinearity, and this could be the problem.

Besides looking at scatterplots and simple linear regressions, you could see what combination of regressors might give you the smallest estimated "variance of the prediction error," as found in econometrics and, for example, in the first few pages at the first link below. That might be helpful here, in my opinion. There are many techniques such as forward and backward elimination, but that is somewhat outside of my areas of expertise.

As for the p-values, even in straightforward situations such as the lone regressor for simple linear regression through the origin, they are still generally misleading when used alone. If you compare the estimated value of a regression coefficient, b, to its estimated standard error, that may give you better and more practically interpretable information. Hopefully the magnitude of b is substantially greater than its estimated standard error.

(Note that 0.05 should not be used as a standard 'significance' level. It depends on the sample size. A power analysis would help. Please see the second link below.)

Best wishes - Jim    

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I have same question if the p value is significant and odd ratio is 0.49 and beta coffiecent - 3.015 . How can i interpret this ??