List of top Mathematics for Economy Questions on Linear regression

Consider a two-variables (x, y) linear regression model
\[ y = \alpha + \beta x + \epsilon \] where x and y are the parameters, and \( \epsilon \) is the error term. The parameters are estimated using the Ordinary Least Squares (OLS) method. Let \( \hat{\beta} \) denote the estimated value of \( \beta \). If \( \hat{\beta} = 0 \), then which one of the following statements is CORRECT?

The linear system of equations
𝑥 + 𝑦 = 3,
$𝑥 + (𝑘^2 − 8)𝑦 = 𝑘, 𝑘 ∈ 𝑅$
has no solution for 𝑘 = _____ (in integer).