This paper proposes a simple measure of instrument relevance in multivariate linear models. Instrument relevance, defined as the correlation between instruments and explanatory variables, is crucial for the performance of the instrumental variables (IV) estimator. In univariate models, the R-squared from regressing the endogenous variable on the instrument vector is a useful measure of relevance. However, in multivariate models, this measure can be misleading because it does not account for the correlation structure among explanatory variables. The paper introduces a partial R-squared measure that addresses this issue by focusing on the component of the explanatory variable orthogonal to other explanatory variables and the component of its projection on the instruments orthogonal to the projection of other explanatory variables on the instruments. The paper shows that the partial R-squared measure can be computed using a series of simple OLS regressions. It also discusses the implications of low instrument relevance in multivariate models, including increased inconsistency of IV estimates, larger asymptotic standard errors, and potential departures from the asymptotic normal distribution in finite samples. The paper presents Monte Carlo evidence showing that low instrument relevance can lead to biased IV estimates, fat tails, and oversized hypothesis tests. It also provides an empirical example using US manufacturing data to illustrate the application of the partial R-squared measure. The paper concludes that while partial R-squared can be a useful tool for assessing instrument relevance, it should be used carefully, as pretesting instruments for relevance can lead to inconsistent estimates. The paper also suggests that partial R-squared can be used as a diagnostic tool or as a guiding principle in instrument selection.This paper proposes a simple measure of instrument relevance in multivariate linear models. Instrument relevance, defined as the correlation between instruments and explanatory variables, is crucial for the performance of the instrumental variables (IV) estimator. In univariate models, the R-squared from regressing the endogenous variable on the instrument vector is a useful measure of relevance. However, in multivariate models, this measure can be misleading because it does not account for the correlation structure among explanatory variables. The paper introduces a partial R-squared measure that addresses this issue by focusing on the component of the explanatory variable orthogonal to other explanatory variables and the component of its projection on the instruments orthogonal to the projection of other explanatory variables on the instruments. The paper shows that the partial R-squared measure can be computed using a series of simple OLS regressions. It also discusses the implications of low instrument relevance in multivariate models, including increased inconsistency of IV estimates, larger asymptotic standard errors, and potential departures from the asymptotic normal distribution in finite samples. The paper presents Monte Carlo evidence showing that low instrument relevance can lead to biased IV estimates, fat tails, and oversized hypothesis tests. It also provides an empirical example using US manufacturing data to illustrate the application of the partial R-squared measure. The paper concludes that while partial R-squared can be a useful tool for assessing instrument relevance, it should be used carefully, as pretesting instruments for relevance can lead to inconsistent estimates. The paper also suggests that partial R-squared can be used as a diagnostic tool or as a guiding principle in instrument selection.