Estimation of Biresponse Multipredictor Model using Local Linear Estimator in Case of Scholastic Aptitude and Islamic Tests Modeling

Abstract

Scholastic aptitude test (SAT) and Islamic test are tests that used by state Islamic colleges (SIC) in Indonesia to select new students on the admission test. Both of them are taken from the same subjects, so they are correlated each other. The behavior patterns of both test scores are change because they were observed from 2016 to 2018. In that period, SAT and Islamic test scores of SIC in western Indonesia are higher than those in eastern Indonesia. So the locally modeling is appropriate for this case. There is a significant correlation between both of the tests then they can be modeled simultaneously by using biresponse nonparametric model. In this research, estimating parameter of biresponse multipredictor nonparametric regression model by using weighted least square method. The results show that in average, the increasing public senior high schools percentage and first choice percentage would increase the SAT scores and Islamic test scores of SIC in western Indonesia. Otherwise, in eastern Indonesia the increasing public senior high school percentage and first choice percentage would decrease the SAT scores and Islamic test scores. It means that there are different patterns of SAT and Islamic test scores between western Indonesia and eastern Indonesia.