Please see the attached image for the question. Thx.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Please see the attached image for the question. Thx.
![### Deriving the ANOVA Formula: SST = SSB + SSW
In 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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F048330fb-37a4-4649-bc7e-2ea6f54a2a1a%2Fabbdd2c6-4d83-438c-b834-2de6b5d4a242%2Fwheqds_processed.jpeg&w=3840&q=75)
Given that the sum of within squares is,
The sum of between squares is,
The total sum of squares is,
Step by step
Solved in 2 steps with 4 images
