How to find the "best predicting" variable, if the dependent and independent variables are not really correlated? Here is a short explanation of my problem:
My data:

*

*9 independent variables

*1 dependent variable

In theory, the variables should be linear (the higher the independent variable, the higher the dependent variable). The correlation between the independent and dependent variables however are rather low (cause in reality the dependent variable is affected by many other factors).
What I want: Find out if any of the independent variables could predict the dependent variable.
What I did: I tried running a single linear regression and a multiple linear regression (combinations of the indipendent variables). None of the independent variables could accurately predict the dependent variable (not alone, not as combinations).
My question: Is this valid? Are these results due to the fact that the data is poor (meaning the dependent variable is affected by so many other factors I do not know about)? Or do I have to find another approach to find the "best predicting" variable?
If yes, which approach could I use?
(I am working with R)

In a linear model, the t-statistic show us if there is a significant linear relation between the independent variable. If the t-statistic is close to zero, there is no linear relation or the linear relation is so weak that can not been proven.
