Multiple Regression - Found a Significant model but one variable does not significantly predict the behaviour, how to explain this ? Also attaching correlation table.
The F-statistic tests that at least one variable is significant, which is evident in the t-tests for individual variables listed in the output your provided. It doesn't test whether all variables are significantly different from 0 and have no place in the model.
Other than that in linear regression you are holding other variables equal, so it is entirely possible that a variable will no longer be significant once other variables are taken into account; this has to do with multicollinearity. The correlation coefficients by themselves will not hold other values equal. The regression model is guiding you by telling you that after controlling for other variables, one of them is probably redundant.