Interpreting a R^2 in light of a regression coefficient
If I have a regression coefficient of say 0.5 and a R^2 of 0.01 how do I interpret this?
The dependent variable increases by 0.5 for a one unit increase in the independent variable and at the same time the relationship explains only one percent of the overal variance of the dependent variable.
Is that correct?
Also, if we want to decide if an the independent variable is a major cause in variation of the dependent variable then having a low R^2 should indicate that the independent variable is NOT a major cause?
What if the R^2 score is relatively low (like 0.01) but the coefficient of the regression is relatively high ( like 3.9) ? How would you interpret that?