The songwriting duo of John Lennon and Paul McCartney, the two founding members of the Beatles, composed some of the most popular and memorable songs of the last century. Despite having authored songs under the joint credit agreement of Lennon-McCartney, it is well-documented that most of their songs or portions of songs were primarily written by exactly one of the two. Furthermore, the authorship of some Lennon-McCartney songs is in dispute, with the recollections of authorship based on previous interviews with Lennon and McCartney in conflict. For Lennon-McCartney songs of known and unknown authorship written and recorded over the period 1962-66, we extracted musical features from each song or song portion. These features consist of the occurrence of melodic notes, chords, melodic note pairs, chord change pairs, and four-note melody contours. We developed a prediction model based on variable screening followed by logistic regression with elastic net regularization. Out-of-sample classification accuracy for songs with known authorship was 76\%, with a $c$-statistic from an ROC analysis of 83.7\%. We applied our model to the prediction of songs and song portions with unknown or disputed authorship.