Complex impedance measurements are widely used to characterize superconducting transition edge sensors (TESs) in bolometers and microcalorimeters. Typically, models are fit to impedance data to find parameters which pertain to the performance of these detectors. After the parameters are determined, the models are then used to compute the response and noise of these devices. In this paper, we present general relationships between the measured impedance, the thermal response to power in the TES, and noise. We describe a method for measuring αI and βI of the superconducting phase transition, which does not require model fitting. We find bolometer response is determined from the impedance provided that the absorber is strongly coupled to the TES electron system. We also demonstrate how to calculate upper and lower limits on the noise directly from the impedance data without modeling. Additionally, the relations can be used to check the validity of the models and to understand what information can and cannot be obtained from measurements of impedance, response, and noise.