A receiver in a two-node system is required to make a decision of relevance as to received information, using side information that may or may not be correlated with the received signal. In case the information is judged to be relevant, the receiver is then required to estimate the source with average distortion D. Focusing on the case of testing against independence, a single-letter expression for the rate-error-distortion region is proposed and proven. The resulting region ports a surprising resemblance to a seemingly non-associated classification problem, known as the information-bottleneck. The optimal region is then calculated for a binary symmetric example. Results demonstrate an interesting trade-off between the achievable error-exponent for the decision and the distortion at the decoder.