Check for Multicollinearity in design matrix, compute the Variance inflation factors and the Condition number.

Hello Srikanth,

There are several possible reasons. Debopam is correct in noting that redundancy among the predictors could be an issue. As well, if the total sample size is small to modest, it could be the case that you have insufficient statistical power for the test of individual IV regression coefficient being equal to zero. If the overall model (4-predictor) F-ratio was not large, this could have been the case.

Here's more answers on essentially the same question from a previous thread: https://www.researchgate.net/post/Regression_is_my_analysis_NOT_producing_WEIRD_results

Good luck with your work!

Multiple correlation of the variables is significant whereas the partial correlations are not. This is as a result of multicollinearity and/or cointegration among the variables.

Well, "significance" is a nebulous concept.  Sample size with regard to variance is important.

Perhaps you should try estimating the variances of prediction errors.  Also, you could save out some data to see how well you would have predicted for them.  You could try different models, and compare results.

Multicollinearity

If the model is significant, you may use it in spite of the individual independent variables not being significant. It means that your four IVs are jointly significant. Possible alternative approaches are stepwise regression, all possible subsets regression or in some disciplines they do principal components analysis and do the regression on the first few components