Moderate# The Effect of Rescaling on R-squared

EMETRC-XGV1G4

Suppose you estimate the following statistical model:

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

...obtaining an $R^2$ value of $0.13$. Later, you decide to change the scale of your data, creating a third variable, $z_i = 2.4 \times x_i$.

You then estimate the model using the $z$ variable instead of the $x$ variable:

$$y_i = \beta_0^z + \beta_1^z z_i + \varepsilon_i.$$

What $R^2$ value do you get for the new model?