Financial Risk Manager Part 1
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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:
- Total sum of squares,
- Regression sum of squares,
- Residual sum of squares,
This implies that:
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NNikitesh
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
Explanation:
Explanation
In regression analysis:
- Total Sum of Squares (SST) = 3.125: This represents the total variability in the dependent variable (fetal weight).
- Regression Sum of Squares (SSR) = 2.925: This represents the variability explained by the regression model (the relationship with weeks of gestation).
- 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.
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