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एक विश्लेषक तीन चरों, खपत (C), बचत (S) और कुल आय (TI) पर अवलोकनों के मानकीकृत मानों पर विचार करता है ताकि उनके शून्य माध्य और इकाई प्रसरण हों। वह आगे प्रयोज्य आय (DI) पर विचार करती है जहाँ DI = C + S। TI पर DI, C पर DI और TI पर S के सरल रैखिक समाश्रयण में, समाश्रयण गुणांक क्रमशः 0.8, 0.5 और 0.4 हैं। 21 प्रतिदर्श अवलोकन हैं। प्रतिदर्श सहसंबंध और प्रसरण 20 भाजक के साथ गणना किए जाते हैं। फिर, S पर DI के समाश्रयण में वर्गों के अवशिष्टों के योग का मान है

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  1. 5
  2. 10
  3. 15
  4. 20

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Option 3 : 15
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संप्रत्यय:

अवशिष्ट प्रसरण:

अवशिष्ट प्रसरण DI में प्रसरण के उस भाग का प्रतिनिधित्व करता है जिसे S पर DI के समाश्रयण में स्वतंत्र चर S द्वारा समझाया नहीं गया है।

वर्गों के अवशिष्टों का योग (SSR) की गणना इस प्रकार की जाती है

, यहाँ जितना कम होगा SSR उतना ही कम होगा, जिसका अर्थ है कि मॉडल डेटा में अधिक भिन्नता की व्याख्या करता है।

R2R2Unknown node type: spanR2Unknown node type: spanR2Unknown node type: span

SSR=(1−R2)xकुल वर्गों का योग.
SSR=(1−R2)xकुल वर्गों का योग.SSR=(1−R2)xकुल वर्गों का योग.
SSR=(1−R2)xकुल वर्गों का योग.
SSR=(1−R2)xकुल वर्गों का योग.Unknown node type: span
SSR=(1−R2)xकुल वर्गों का योग.Unknown node type: spanSSR=(1−R2)xकुल वर्गों का योग.Unknown node type: span

व्याख्या:

चूँकि चर शून्य माध्य और इकाई प्रसरण के साथ मानकीकृत हैं, DI का कुल प्रसरण C और S के बीच विभाजित किया जा सकता है:



समाश्रयण मॉडल गुणांकों के साथ दिया गया है:

TI पर DI: गुणांक 0.8 है।, C पर DI: गुणांक 0.5 है और TI पर S: गुणांक 0.4 है।

S पर DI के समाश्रयण के लिए अवशिष्ट प्रसरण (त्रुटि) DI पर S के समाश्रयण गुणांक से संबंधित है,

जो सीधे नहीं दिया गया है लेकिन अन्य आँकड़ों से अनुमान लगाया जा सकता है।

वर्गों के अवशिष्टों का योग आमतौर पर इस प्रकार गणना किया जाता है

यहाँ, S पर DI के समाश्रयण के लिए निर्धारण का गुणांक है, लेकिन प्रदान किए गए के आधार पर

समाश्रयण गुणांक, हम मान सकते हैं कि इस मामले में अवशिष्ट प्रसरण वर्गों के 15 अवशिष्टों के योग की ओर ले जाता है।

इसलिए, सही उत्तर 3) है।

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