For reasons outlined in the text, we made several modifications in applying the optimal linear model analysis from Kaufman et al. (2014) to ask the question: does preparatory activity evolve in a way that predicts movement? Here we present a supplementary analysis that is more congruent with the analysis performed in the Kaufman et al. paper. First, we used only the data from the single-direction blocks of trials, instead of fitting to the 8-direction blocks and predicting the data from the single-direction blocks as we had done before. Second, we performed PCA on the neural data before fitting to movement parameters. In this way the W from equation (3) is now solved from the equation , where is the lower-dimensional representation of the neural population response during the movement epoch obtained from PCA. E is the eye velocity (A and B) or eye speed (C and D) from the single-direction pursuit task. We are fortunate that the kinematics of the movement uniquely reflect the action of the extraocular eye muscles and are already low-dimensional (2-dimensional for velocity, 1-dimensional for speed). Therefore, we did not need to perform PCA on the movement data (E). In accordance with Kaufman et al. (2014) we chose the dimensions of based on the movement dimensions in order to have an equal number of dimensions in the row and null space of the weight matrix. For fitting to eye velocity and speed, we chose the dimensionality of to be 4 and 2, respectively. We then projected the low-dimensional representation of the neural population response during the preparatory epoch of the single-direction pursuit task onto the row and null spaces of W. Because the curves in panels A and C deviated from zero systematically, our supplementary analysis reaches the same conclusion as Figures 5 and 6: preparatory activity evolves in a way that predicts movement when there is none. In the words of Kaufman et al. (2014), FEFSEM preparatory activity is not confined to the null space. (A), (B) Solid and dashed traces plot the projection of the low-dimensional representation of population preparatory activity onto the row (A) and null (B) spaces of the weight matrix obtained from fitting to horizontal (solid) and vertical (dashed) eye velocity. (C), (D) Solid and dashed traces plot the projection of the low-dimensional representation of population preparatory activity onto the row (C) and null (D) spaces of the weight matrix obtained from fitting to eye speed. In both analyses, the magnitude of projection of preparatory activity onto the null space increase very early in fixation and decays back to zero as preparation progresses. In contrast, the projection onto the row space steadily increases as preparation progresses. Importantly, the prediction for eye velocity and speed obtained by projection onto the row space is in the direction of the ensuing target motion (0 degrees, right) and positive, respectively.