You can't overfit a linear regression. Overfitting is basically where you have your model go through, or mostly through, your data points. For example if you had 4 data points and fit a cubic, that would be overfitting. If you have N data points and fit a polynomial with, oh I don't know, say, N/2 or something, then you might have over fitting. But that won't happen with a line since it won't go through all your data points unless you had only 2 points.
It could be that your data does not fit the model that was determined using the 70% of other points, but I doubt it since you probably chose them randomly. I'd think the 30% error was much worse than the other 70% just due to randomness. In general (usually) testing/validation will be worse error than the training points, but it could be better.