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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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 ordinary least squares (OLS) regression analysis:
- Total Sum of Squares (SST) = 3.125 represents the total variability in the dependent variable (foetal weight)
- Regression Sum of Squares (SSREG) = 2.925 represents the variability explained by the model
- Residual Sum of Squares (SSRES) = 0.2 represents the variability unexplained by the model
The relationship between these components is: SST = SSREG + SSRES
Why C is correct:
- SSREG (2.925) measures how much of the total variability in foetal weight is explained by the number of weeks of gestation
- This represents the portion of variation that can be attributed to the relationship between the variables
Why other options are incorrect:
- A: 0.2 is SSRES, which is the unexplained variability, not the explained variability
- B: 3.125 is SST, which is the total variability, not the unexplained variability
- D: 3.125 is SST, which includes both explained and unexplained variability, not just the explained portion
The high SSREG value (2.925 out of 3.125 total) indicates that the model explains most of the variability in foetal weight, suggesting a strong relationship with weeks of gestation.
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