Consider the regression of T1 on both M1 and M2:5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\text{T}}_{ 1} = \beta_{0} + \beta_{ 1} *{\text{M}}_{ 1} + \beta_{2} * {\text{M}}_{ 2} $$\end{document}where β 0 denotes the intercept, and β 1 and β 2 denote the regression weight of M1 and M2, respectively. Regression weight β 1 is a measure of the relationship between T1 and M1 while controlling for M2, and is in the completely standardized case calculated as6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \beta_{1} = \frac{{r_{t1,m1} - r_{t1,m2} r_{m1,m2} }}{{1 - r_{m1,m2}^{2} }}. $$\end{document}
