Çok katlı regresyon analizinde kürecikler yöntemi ve bir uygulama

Abstract

Multiple regression analysis is one of the statistical approach to prediction. In this analysis, one or more independent variables or predictors are selected along with one dependent variable. Using scors on these variables, it is possible to determine the least squares regression weights that minimize the squared distance between the predicted and actual values on the dependent variable.lt is also possible to predict with a certain degree of accuracy by using regression equation derived from the sample. If the interest of researchers lies in individual predictors standardized regression coefficient Cbeta weightsDis used to measure the importance of a predictors. These coefficients reflect the strength and direction of the relationship between the predictor variables and dependent variable. However,if the predictors are highly correlated,it is very difficult to determine the relative influence of each predictors on the dependent variable. This situation is called "Multicollinearity". When two or more predictors are highly correlated »they are measuring the same thing since much of the variance of one predictor is tibeing shared by the other. When one or more predictors are linear combinations of the remaining predictors, exact multicollinearity exists »thus it is impossible to derive the unique estimates of the regression coefficients. The major effects of mul ti col linearity are described as follows: ID High variance of coefficients may drastically reduce the precision of estimation. 2D Esti mates of coefficients may be sensitive to particular sets of sample data. 3D Mul ti col linearity can result in coefficients appearing to have the wrong sign or opposite to the prior expectations of the researchers. 4DSome variables may be dropped from the model because they are not significant in the sample even thought they are important in the populations. Ridge Regression is a technique of developing the estimators of regression coefficients to remedy the mul ti col linearity problem. Ridge estimators are obtained by adding a constant into the normal equations and forcing the resulting estimators to be biased. When an estimators has only a small bias, but it is substantially more precise than an unbiased estimator, it may be preferred since it will have a a greater probability of being close to the true parameter value. A measure of the combined effects of bias and sampling illvariation is th© expected value of the squared deviation of the biased estimator from the true parameter ft. This measure is called "mean squared error" of the estimator and it can be shown that EC/XJO -ft! =VC^Ck:0 + CEC/3C10 -ftj Morever, the mean squared error equals the variance of estimator plus the squared bias. If the estimator is unbiased, the mean squared error CMSED is identical to the variance of the esti mat or. The biased estimator can give a smaller mean squared error than the ordinary least squares COLSD estimator if the squared bias is no longer than the reduction achived in variance. This is the main aim of ridge regression. There were a few main purposes of this study. The first purpose was to demonstrate how ridge regression can be applied to data studied. The secondary purpose was to compare the characterictics and performance of the ridge methods versus the OLS methods. Al so, other purpose is to use the principle component analysis together the ridge regression to study the sample data.