correlation = 0.3, is not bad at all, especially when you have more than 1 predictors.
The part you should be care about is the meaning of F and T test.
If the test is significant, that just mean for the data you have at your hand, you don't have enough evidence to reject the H0 : \alpha_1=0 ,  \alpha_2=0, \alpha_3=0, \alpha_4=0(F), or H0:\alpha_i =0(T)  F=(ssr/df)/sse/df
You should check the assumption as while.
Also, whether this is a good fit or not, you may look at the R-adj, aic or PRESS score.
I bet you have  a good model Brother!

1.不应只看系数，应该看p值是否<0.05，即是否通过了显著性检验
2.四个自变量之间可能存在多重共线性