Many textbooks and articles (such as this one) advise to standardize variables before entering them into our regression models; i.e., (variable - mean) / standard deviation
However, I just came across a counter example. How do you rationalize this?
Let's say: $$Y = 2X$$ $$X = \{-3, -2, -1, 0, 1, 2, 3 \}$$ $$Y = \{-6, -4, -2, 0, 2, 4, 6 \}$$ After standardizing, $$X_{sd} = \{-1.3887301, -0.9258201, -0.46291, 0.0, 0.46291, 0.9258201, 1.3887301 \}$$ $$Y_{sd} = \{-1.3887301, -0.9258201, -0.46291, 0.0, 0.46291, 0.9258201, 1.3887301 \}$$ $$\Rightarrow Y_{sd} = X_{sd}$$ So, in this example, if we standardize the variables, the desired slope (i.e., the effect size) vanishes!!!