Excel linest formula for weighted polynomial fit -

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एक्सेल सिलेस्ट भारित बहुपक्षीय फिट फार्मूला को कैसे निर्दिष्ट करें, जैसे LINEST (y * w ^ 0.5, IF ({ 1,0}, 1, x) * w ^ 0.5, गलत, सच), लेकिन यह रैखिक फिट के लिए है मैं दूसरे आदेश और तीसरे क्रम बहुपद प्रतिगमन फिट के लिए समान सूत्र की तलाश कर रहा हूं।

एक दृष्टिकोण में अन्य पद पहले से ही भारित बहुपदों के लिए सुझाव दिया गया था। उदाहरण के लिए एक 4x1 रेंज में CTRL + SHIFT + ENTER के साथ क्यूबिक फिट के लिए प्रयास करें: 

  = LINEST (y * w ^ 0.5, (x-1E-99) ^ {0,1, 2,3} * w ^ 0.5, FALSE)   
 (- 1e-99 यह सुनिश्चित करता है कि 0 ^ 0 = 1)। आर ^ 2 के लिए रैखिक मामले की कोशिश करें:  
  = INDEX (LINEST ((y-SUMPRODUCT (वाई, डब्ल्यू) / एसएम (डब्ल्यू)) * w ^ 0.5, (x-1E -99) ^ {0,1,2,3} * w ^ 0.5, FALSE, TRUE), 3,1)   
  व्युत्पन्न   
 मानक कम से कम वर्गों में हम वेक्टर  b  को कम से कम प्राप्त करते हैं:  | y-Xb | एक² = (y-Xb) '(y-Xb)' (y-Xb)   
 भारित मामले में  b  को इसके बजाय कम से कम करने के लिए चुना जाता है:  | W (y-Xb) | एक² = (y-Xb) 'W'W (y-Xb) < / कोड>  
 तो भारित प्रतिगमन  Wy  पर  WX  है, जहां  W'W = w ²  का विकर्ण मैट्रिक्स है वजन

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