We present an application of data analytics and supervised machine learning to allow accurate predictions of the macroscopic stiffness and yield strength of a unidirectional composite loaded in the transverse plane. Predictions are obtained from the analysis of an image of the material microstructure, as well as knowledge of the constitutive models for fibres and matrix, without performing physically-based calculations. The computational framework is based on evaluating the 2-point correlation function of the images of 1800 microstructures, followed by dimensionality reduction via principal component analysis. Finite element (FE) simulations are performed on 1800 corresponding statistical volume elements (SVEs) representing cylindrical fibres in a continuous matrix, loaded in the transverse plane. A supervised machine learning (ML) exercise is performed, employing a gradient-boosted tree regression model with 10-fold cross-validation strategy. The model obtained is able to accurately predict the homogenized properties of arbitrary microstructures.