Please see the attached image for the question. Thx. ### Deriving the ANOVA Formula: SST = SSB + SSWIn an analysis of variance (ANOVA), the total variation in the data is partitioned into components: variation between groups and variation within groups. The ANOVA formula can be expressed as the sum of three sums of squares functions:1. **SSW (Sum of Squares Within groups):** \[ \text{SSW} = \sum_{i=1}^{k} \sum_{j=1}^{n_i} (Y_{ij} - \bar{Y}_{i.})^2 \] This expression represents the sum of the squared deviations of each observation \( Y_{ij} \) from its respective group mean \( \bar{Y}_{i.} \).2. **SSB (Sum of Squares Between groups):** \[ \text{SSB} = \sum_{i=1}^{k} n_i (\bar{Y}_{i.} - \bar{Y}_{..})^2 \] Here, the expression represents the sum of the squared deviations of each group mean \( \bar{Y}_{i.} \) from the overall mean \( \bar{Y}_{..} \), multiplied by the number of observations \( n_i \) in each group.3. **SST (Total Sum of Squares):** \[ \text{SST} = \sum_{i=1}^{k} \sum_{j=1}^{n_i} (Y_{ij} - \bar{Y}_{..})^2 \] This represents the sum of the squared deviations of each observation \( Y_{ij} \) from the overall mean \( \bar{Y}_{..} \).In the context of ANOVA, the formula SST = SSB + SSW is used to partition the total variation into variation due to differences between group means (SSB) and variation within groups (SSW).

Name: Please see the attached image for the question. Thx. ### Deriving the
Uploaded: 2024-03-05T11:52:21.000Z
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Description: Please see the attached image for the question. Thx. ### Deriving the ANOVA Formula: SST = SSB + SSWIn an analysis of variance (ANOVA), the total variation in the data is partitioned into components: variation between groups and variation within grou