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This is called an opportunity for restructuring your regression equation. For example, why not do this: $$GDP/Pop = \beta_0 + \beta_2 X_2 + \beta_3 X_3$$ Then you only have to multiply to the population to get GDP estimates. OR $$log(GDP / Pop) = \beta_0 + \beta_2 X_2 + \beta_3 X_3$$ which is effectively: $$log(GDP) = log(Pop) + \beta_0 + \beta_2 X_2 + ... 1 Coefficient change Let some there be some data distributed according to a quadratic curve:$$y \sim \mathcal{N}(\mu = a+bx+cx^2, \sigma^2 = 10^{-3})$$For instance with x \sim \mathcal{U}(0,1) and a=0.2, b=0 and c=1. Then a linear curve and a polynomial curve will have very different coefficients for the linear term. set.seed(1) x <- runif(100, 0,... 3 The ordinary least squares solution is simply given by:$$\beta = (X'X)^{-1}X'y Let's imagine we augment $X_{n\times p}$ with one or more variables $\tilde X_{n\times \tilde p}$, appending its corresponding values as columns, and call the resulting matrix ${X^*}_{n\times p^*}$, $p^* = p + \tilde p$. Now, given enough degrees of freedom, coefficients will ...