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Cells respond to their environment by modulating protein levels through mRNA transcription and post-transcriptional control. Modest observed correlations between global steady-state mRNA and protein measurements have been interpreted as evidence that mRNA levels determine roughly 40% of the variation in protein levels, indicating dominant post-transcriptional effects. However, the techniques underlying these conclusions, such as correlation and regression, yield biased results when data are noisy, missing systematically, and collinear---properties of mRNA and protein measurements---which motivated us to revisit this subject. Noise-robust analyses of 24 studies of budding yeast reveal that mRNA levels explain more than 85% of the variation in steady-state protein levels. Protein levels are not proportional to mRNA levels, but rise much more rapidly. Regulation of translation suffices to explain this nonlinear effect, revealing post-transcriptional amplification of, rather than competition with, transcriptional signals. These results substantially revise widely credited models of protein-level regulation, and introduce multiple noise-aware approaches essential for proper analysis of many biological phenomena.