Regression Coefficients – Problems, Properties & Solutions
Regression Coefficients – Problems, Properties & Solutions 🔹 1️⃣ Meaning of Regression Coefficients In simple linear regression: Y = a + b y x X Y = a + b_{yx}X Y = a + b y x X b y x b_{yx} b y x = Regression coefficient of Y on X b x y b_{xy} b x y = Regression coefficient of X on Y They measure the rate of change of one variable with respect to the other. 🔑 Important Properties of Regression Coefficients Same Sign Property Both b y x b_{yx} b y x and b x y b_{xy} b x y have the same sign as correlation (r). Product Rule b y x ⋅ b x y = r 2 b_{yx} \cdot b_{xy} = r^2 b y x ⋅ b x y = r 2 Correlation Relation r = ± b y x ⋅ b x y r = \pm \sqrt{b_{yx} \cdot b_{xy}} r = ± b y x ⋅ b x y Independent of Change of Origin Regression coefficients do not change if origin changes. Not Independent of Scale They change if scale changes. If one regression coefficient is greater than 1 , the other must be less than 1 . 🔢 Pr...