Linear Regression vs. Hypothesis Testing

[fahdguthmy]

I need help understanding the significance of performing both linear regression and ANOVA on the same data. In this case:
1) I got an extremely low R² value for linear regression meaning the independent variable (income) does not explain the variance in the dependent variable (emissions);
2) I conducted an ANOVA test and result is not significant (0.001 p-value at alpha 0.01) meaning there are differences between the income levels.

I'm assuming I didn't interpret the results wrong.. My problem is that I don't quite understand the implications of these results.
-How does each of the two methods add value to my research?
-Is there something I can deduce from one result that I cant from the other?
-Was there any additional value in doing two as opposed to just sticking to one?

Thanks for the consideration.