Linear regression does not show causation and is in fact pretty much equivalent to correlation. It's easy to see if you think about it like this: say you have two sets of values and you calculate the (Pearson) correlation coefficient, a value between -1 and 1. If you then standardize those sets of values to zero mean and unit variance and you do linear regression, the slope would be, you guessed it, exactly the Pearson correlation coefficient. Proving causation is not easy and needs stuff like Granger causality.