We study inference for the fraction of total response variation explained by multivariate high-dimensional linear models. Two moment equations yield explicit estimates without fitting the regression coefficients. We establish asymptotically valid confidence intervals for fixed- and random-effects models, allowing the response dimension to grow with the sample size. The theory describes how response dependence affects precision and provides a correction for unequal noise levels in the random-design setting. Simulations assess finite-sample performance, and an analysis of yeast growth across environments illustrates joint inference for additive marker-based signal.

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