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\[\textrm{Var }\hat{\beta}_{0}=\frac{\sigma^{2}\sum_{i=1}^{n}x…
\[\textrm{Var }\hat{\beta}_{0}=\frac{\sigma^{2}\sum_{i=1}^{n}x_{i}^{2}}{n\sum_{i=1}^{n}x_{i}^{2}-\left(\sum_{i=1}^{n}x_{i}\right)^{2}}\]\[\textrm{Var }\hat{\beta}_{1}=\frac{n\sigma^{2}}{n\sum_{i=1}^{n}x_{i}^{2}-\left(\sum_{i=1}^{n}x_{i}\right)^{2}}\]\[\textrm{Cov}(\hat{\beta}_{0},\hat{\beta}_{1})=\frac{-\sigma^{2}\sum_{i=1}^{n}x_{i}}{n\sum_{i=1}^{n}x_{i}^{2}-\left(\sum_{i=1}^{n}x_{i}\right)^{2}}\]
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