About question 1.1 of https://arxiv.org/pdf/1509.09169.pdf
Here are two sorts of $X$, namely a bold one and a normal one. Usually when I see a regression equation I see $Y = \mbox{**X**}\beta$, but can't use it in this situation. Here they write $Y = \beta_0 + \beta_1X$ and they don't define X.
Does anyone have a definition of which he knows that this is probably what they mean?
In $Y = X\beta + \epsilon$ notations, $X$ is an $n\times p$ matrix, while in $ Y = \beta_0 + \beta X + \epsilon$, $X$ usually denotes variable (not necessarily random). In your case, they explicitly stated that $X$ is a variable that were sampled $8$ times, namely its values were $X=(−2, −1, −1, −1, 0, 1, 2, 2)^⊤$.