Multivariate linear regression was used to investigate the effect of Day 0 progesterone, Day 7 progesterone, BCS, grade, and DPP on the Day 7 gene expression and Day 7 embryo size. Relationships were determined on the log10 transformed Day 7 gene expression and embryo size data (a second multivariate linear regression analysis was also conducted to investigate the effect of Day 7 embryo size on the Day 7 gene expression). The analysis was based on the 81 genes with gene expression greater than the limit of detection of the assay (genes with an average log10 gene expression less than 0.6 were deemed to be below the limit of detection of the assay and largely measurement noise). The model characterizes a d-dimensional continuous response vector as a linear combination of predictors (K − 1) and an error vector that is multivariate normal distributed. For the ith observation, the multivariate linear regression model for the d × 1 response vector is