Difficult# Rescaling and the Sum of Squared Residuals

EMETRC-EGJWCP

Suppose you are using the Simple Linear Regression Model:

$$y_i = \beta_0 + \beta_1 x_i + u_i$$

...which you estimate via OLS. Further suppose that you decide to rescale one of the variables (for example, changing it from kilometers to meters). Because of the rescaling, the estimated OLS slope term coefficients of the original and rescaled models will not be equal.

Since OLS estimates are determined by the minimization the sum of the squared residuals (SSR), this implies that the SSR **must** have changed after the rescaling, as well.

This statement is: