METODE RANK NONPARAMETRIK  PADA MODEL REGRESI LINEAR 

ABSTRACT Kusuma, 2007. NONPARAMETRIC RANK METHOD ON LINEAR REGRESSION MODEL. Faculty of Mathematics and Natural Sciences. Sebelas Maret University. The equation 0 1 1 2 2 k k Y X X X b b b b e = + + + + + L is a model of a linear regression with i b are regression parameters which are estimated based on the observations of data. The least square method is a method to estimate the regression parameters that gives an optimal result if the error terms assumed have normally distributed, ( ) 2 , 0 ~ s e N . If the normality assumption is not satisfied then estimation of regression parameters is not exact. The violation of normality assumption is indicated by the occurence of outliers. The nonparametric rank method can be used to analyze the data if the errors have not normally distribution which indicated by the occurence of outliers. The aims of the final project are to estimate the regression parameters and to test the significance of regression parameters to know the relationship of independent variable with dependent variable, using the method of nonparametric rank. The method used in this final project is a literary study. Based on the discussion, it can be concluded that estimation of regression parameters is obtained by minimizing the sum of rank – weighted residuals. The hypothesis used on simple linear regression is 0 : 0 = b H versus 0 : 1 ¹ b H with the test statistics ( ) U SD U t = . The zero hypothesis 0 H is rejected when a < p where p = Prob [ ] t T ³ and p value is obtained by using t distribution table with n – 2 degrees of freedom. On the mulitiple linear regression, the hypothesis used is 0 1 : 0 l k H b b + = = = L versus 1 1, , : 0 l k H b + ¹ K with the test statistics ( ) tereduksi penuh rank JRSB JRSB F k l ct Ÿ - = - . The zero hypothesis 0 H is rejected when a < p where p = Prob [ ] rank F F ³ and p value is obtained by using F distribution table with k – l and n – k – 1 degrees of freedom