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Answer: The variability explained by the model is 2.925
## Explanation In regression analysis: 1. **Total Sum of Squares (SST)** = 3.125: This represents the total variability in the dependent variable (fetal weight). 2. **Regression Sum of Squares (SSR)** = 2.925: This represents the variability explained by the regression model (the relationship with weeks of gestation). 3. **Residual Sum of Squares (SSE)** = 0.2: This represents the variability unexplained by the model (random error). **Key relationships:** - SST = SSR + SSE - 3.125 = 2.925 + 0.2 **Interpretation:** - The variability **explained** by the model is SSR = 2.925 - The variability **unexplained** by the model is SSE = 0.2 - The **total variability** is SST = 3.125 Therefore, option C is correct because 2.925 represents the variability explained by the regression model. **Why other options are incorrect:** - **Option A (0.2)**: This is the unexplained variability (residual sum of squares), not the explained variability. - **Option B (3.125)**: This is the total variability, not the unexplained variability. - **Option D (3.125)**: This is the total variability, not the explained variability.
Author: Nikitesh Somanthe
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Ordinary least squares is used to estimate the relationship between foetal weight and the number of weeks of gestation in a group of women. The exercise gives the following results:
This implies that:
A
The variability explained by the model is 0.2
B
The variability unexplained by the model is 3.125
C
The variability explained by the model is 2.925
D
The variability explained by the model is 3.125