Least squares with a balanced plus-minus design

A simple linear regression model $Y_i=\beta_0+\beta_1 x_i+\epsilon_i$, with $x_i=(-1)^i$ for $i=1,2,…,20$, is fitted. The random error variables $\epsilon_i$ are uncorrelated with mean $0$ and finite variance $\sigma^2>0$. Let $\hat\beta_0$ and $\hat\beta_1$ be the least squares estimators of $\beta_0$ and $\beta_1$ respectively. Let $\hat Y_i$ be the fitted value of the $i^{\mathrm{th}}$ response variable $Y_i$, for $i=1,…,20$. Which of the following statements is/are correct?