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corrected proof
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P/anova2-ols.md

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@@ -41,7 +41,7 @@ $$ \label{eq:anova2-ols}
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\end{split}
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$$
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where $\bar{y}_{\bullet \bullet \bullet}$, $\bar{y}_{i \bullet \bullet}$, $\bar{y}_{\bullet j \bullet}$ and $\bar{y}_{i j \bullet}$ are the following [sample means](/D/mean-samp):
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where $\bar{y} _{\bullet \bullet \bullet}$, $\bar{y} _{i \bullet \bullet}$, $\bar{y} _{\bullet j \bullet}$ and $\bar{y} _{i j \bullet}$ are the following [sample means](/D/mean-samp):
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$$ \label{eq:mean-samp}
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\begin{split}
@@ -151,4 +151,4 @@ $$ \label{eq:rss-der-gamma-zero}
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\hat{\gamma_{ij}} &= \frac{1}{n_{ij}} \sum_{k=1}^{n_{ij}} y_{ijk} - \hat{\alpha}_i - \hat{\beta}_j - \hat{\mu} \\
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\hat{\gamma_{ij}} &= \frac{1}{n_{ij}} \sum_{k=1}^{n_{ij}} y_{ijk} - \frac{1}{n_{i \bullet}} \sum_{j=1}^{b} \sum_{k=1}^{n_{ij}} y_{ijk} - \frac{1}{n_{\bullet j}} \sum_{i=1}^{a} \sum_{k=1}^{n_{ij}} y_{ijk} + \frac{1}{n} \sum_{i=1}^{a} \sum_{j=1}^{b} \sum_{k=1}^{n_{ij}} y_{ijk} \; .
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\end{split}
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$$
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$$

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