Plot the Data First!
Below are four data sets that have the same correlation coefficient r, same r-squared, same slope and intercept of the regression line, same t-test for significance of the slope, etc. Just looking at a number like r-squared to decide if your (here regression) analysis is beneficial is not a good workflow! You could be led astray. The upper left graph is the type of data you might assume occurs. Your data may be quite different than that !
Nothing replaces a good plot to give insight into your data analysis.
Sheather, S. J. (2009). A Modern Approach to Regression with R. Springer, New York.