We study the Hyers-Ulam stability theory of a four-variate Jensen-type functional equation by considering the approximate remainderϕand obtain the corresponding error formulas. We bring to light the close relation between theβ-homogeneity of the norm onF∗-spaces and the approximate remainderϕ, where we allowp,q,r, andsto be different in their Hyers-Ulam-Rassias stability.