OLS identities for five design points

Consider a simple linear regression model $Y_{i}=\beta_{0}+\beta_{1}x_{i}+\epsilon_{i}$, $i=1,2,3,4,5$, where the random errors $\epsilon_{i}$ have mean $0$ and variance $36$, and are uncorrelated. Let $\hat{\beta}_{0}$ and $\hat{\beta}_{1}$ be the least squares estimators of $\beta_{0}$ and $\beta_{1}$, respectively. The above model is fitted to the following dataset

| $x$ | $-2$ | $-1$ | $0$ | $1$ | $2$ | |—|—|—|—|—|—| | $y$ | $2.7$ | $a$ | $-0.1$ | $b$ | $-2.3$ |

where $(a,b)\in\mathbb{R}^{2}$. Which of the following statements is/are true?