The percent explained variation (r 2) of tensile strength iT) of dimension lumber can be accounted for primarily by apparent modulus of elasticity tEa). Tensile strength ratio, a good index of T of structural lumber, and E a are both dependent on relative knot size, making T a function of E a. This theoretical relationship helps to increase r 2 when T is regressed on E a and gives the "cause and effect" for some multiple regression analyses. An independent variable was identified on the basis of this theory. Shortening the gage length enhances ability to predict T when flatwise bending E a or tension E a is used as an independent variable, but not when edgewise bending E a is used. Two single variables not previously reported, E a measured in flatwise bending on 16-inch gage length (EF 16) and E a measured in tension on 6-inch gage length (ET 6) (based solely on deformation measurements), are individually able to explain approximately as much variation of T (r 2 = 0.75) as the combination of E a measured flatwise on 48-inch gage length (span length for the existing American grading machines), and ASTM bending strength ratio. The combination of EF 16 and ET6 can explain 85 % of the variation of T. The highest r 2 (0.87) was obtained when a modified bending strength ratio was added to these new variables.