I want to do a regression. However, I have quarterly data for the dependent variable and only annual data for the independent variable. Is it useful to interpolate the annual data on quarterly data or are the results then not to be used?
You're better off transforming the quarterly response data into yearly response data (probably either sum or mean, depending on your goal) than creating predictor data out of thin air with interpolating the annual into quarterly. Interpolation is invalid for time series data; the results would be useless.