前言
多元廻歸是統計方法中，最被廣泛應用的分析工具。但是最小乘方法有襤用之虞，特別在樣本情報顯示多元共線性嚴重時，最小乘方係數估計值產生：符號錯誤，數值過大及敏感變動的弊病。本文計分五章十七節，探討共線的根源、困擾及判定，並提出偏估計修正方法。
第一章分析問題發生的癥結，如何由樣本資料判定共線的嚴重程度，並比較數種傳統的補救方法。第二章以次，提出建立於均方誤差評估準則的偏估計方法，以導入少許偏誤於估計式及增加殘差平方和為代價，獲取較穩定而可靠的估計值。首先脊廻歸藉擴大相關矩陣XX對角線上元素，以達到降低估計向量長度平方，及縮小係數之估計標準誤的双重目標。第三章主元素廻歸，將原資料矩陣X行正交轉換，剔除少數不重要而嚴重迫害方程式的主元素後再作廻歸，並轉換回原來係數估計式，同樣達到穩定估計值的目的，第四章艾根值廻歸，則是主元素廻歸進一步引申，同時考慮應變數Y對於建立廻歸方程式所發生的作用。由包括Y的擴大相關矩陣之艾根值及艾根向量的幾何意義，剔除無預測價值之艾根向量，以消除共線的影響，並執行剔除變數功能。第五章以虛擬資料比較三種偏估計方法與最小乘方法的係數估計值。最後將上述上法加以綜合並補充之。

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