Truncated Spline Regression to Estimate Regression Curve of Strontium Titanate XRD Data

Abstract

Characterization of ferroelectric material using X-Ray Diffraction tools (XRD) resulted in 2θ degree and intensity of diffraction data. The result of XRD characterization showed that the relationship between 2θ degree and diffraction intensity formed spectrum pattern; fluctuation of diffraction intensity value along with the increasing of 2θ degree. The high fluctuation of diffraction intensity value affected the inconsistency of mean and variance value. Thus the model used to estimate curve shape could not be analysed by parametric method which is strict with assumptions. Spline regression is a polynomial model with segmented character that has high flexibility to generate regression curve estimation through data fitting method. This research used the truncated spline regression model to estimate regression curve of Strontium Titanate (SrTiO3) and SrTiO3 doping with 2 % of RuO2 (SrTiO3+RuO2) XRD data. The best truncated spline regression model to estimate regression curve of SrTiO3 was model with 42 knots. This model has the smallest Akaike’s Information Criterion (AIC) value and the biggest R2, that is 13403.33 and 0.6503 respectively. Meanwhile, the best truncated spline regression model to estimate regression curve of SrTiO3 RuO2 was model with 37 knots. This model has the AIC value of 13953.68 and R2 of 0.6302.