Ensuring the security of sensitive data is an increasingly important challenge for information systems managers. A widely used technique to protect sensitive data is to mask the data by adding zero mean noise. Noise addition affects the quality of data available for legitimate statistical use. This article develops a framework that may be used to analyze the implications of additive noise data masking on data quality when the data is used for regression analysis. The framework is used to investigate whether noise should be added to non-sensitive attributes when only a subset of attributes in the database are considered sensitive, an issue that has not been addressed in the literature. Our analysis indicates that adding noise to all the attributes is preferable to the existing practice of masking only the subset of sensitive attributes.