This paper introduces a model of multiple-instance learning applied to the prediction of aspect ratings or judgments of specific properties of an item from user-contributed texts such as product reviews. Each variable-length text is represented by several independent feature vectors; one word vector per sentence or paragraph. For learning from texts with known aspect ratings, the model performs multiple-instance regression (MIR) and assigns importance weights to each of the sentences or paragraphs of a text, uncovering their contribution to the aspect ratings. Next, the model is used to predict aspect ratings in previously unseen texts, demonstrating interpretability and explanatory power for its predictions. We evaluate the model on seven multi-aspect sentiment analysis data sets, improving over four MIR baselines and two strong bag-of-words linear models, namely SVR and Lasso, by more than 10% relative in terms of MSE.