Estimating r 2 shrinkage in regression

The effectiveness of various analytical formulas for estimating R Shrinkage in multiple regression analysis was investigated. Two categories of formulas were identified estimators of the squared population multiple correlation coefficient ( 2  ) and those of the squared population cross-validity coefficient ( 2 c  ). The authors compeered the effectiveness of the analytical formulas for determining R shrinkage, with squared population multiple correlation coefficient and number of predictors after finding all combination among variables, maximum correlation was selected to computed all two categories of formulas. The results indicated that Among the 6 analytical formulas designed to estimate the population 2  , the performance of the (Olkin & part formula-1 for six variable then followed by Burket formula & Lord formula-2 among the 9 analytical formulas were found to be most stable and satisfactory. Keywords(multiple regression, cross-validity, multiple correlation coefficient, Linear models shrinkage regression, R shrinkage).