Polygenic indexes (PGIs) are DNA-based predictors. Their value for research in many scientific disciplines is growing rapidly. As a resource for researchers, we used a consistent methodology to construct PGIs for 47 phenotypes in 11 datasets. To maximize the PGIs' prediction accuracies, we constructed them using genome-wide association studies-some not previously published-from multiple data sources, including 23andMe and UK Biobank. We present a theoretical framework to help interpret analyses involving PGIs. A key insight is that a PGI can be understood as an unbiased but noisy measure of a latent variable we call the 'additive SNP factor'. Regressions in which the true regressor is this factor but the PGI is used as its proxy therefore suffer from errors-in-variables bias. We derive an estimator that corrects for the bias, illustrate the correction, and make a Python tool for implementing it publicly available.