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QuestionStatistics
"SSE can never be
A. larger than SST
B. smaller than SST
C. equal to 1
D. equal to zero"
12 months agoReport content
Answer
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Step 1:Let me solve this step by step, focusing on the statistical concept of Sum of Squared Errors (SSE) and Total Sum of Squares (SST).
Step 2:: Understanding SSE and SST
- SSE (Sum of Squared Errors) measures the total deviation of predicted values from actual observed values - SST (Total Sum of Squares) measures the total variance in the dependent variable
Step 3:: Recall the Relationship Between SSE and SST
The fundamental relationship is: $$R^{2} = 1 - \frac{SSE}{SST}
Step 4:: Analyzing the Possible Scenarios
- By definition, $$0 \leq \frac{SSE}{SST} \leq 1
- SSE represents the unexplained variation - SST represents the total variation
Step 5:: Evaluating Each Option
A. SSE larger than SST: IMPOSSIBLE B. SSE smaller than SST: POSSIBLE C. SSE/SST equal to 1: IMPOSSIBLE D. SSE equal to zero: POSSIBLE (perfect model prediction)
Final Answer
SSE can NEVER be larger than SST. The key insight is that SSE represents a portion of the total variation (SST), so it cannot exceed the total variation.
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