Confidence Interval of Simple Linear Regression Coefficient with Errors in Variables for Small Sample Sizes

Wisunee Puggard, Manachai Rodchuen, Putipong Bookkamana, Bandhita Plubin


This study aims to improve and compare the confidence intervals of simple linear regression coefficient               ( ) with errors in variables for small sample sizes when the variance of errors in  ( ) is known. Improved ordinary least square confidence interval (IOLS) is the new developing method which improved from ordinary least square confidence interval. Comparing IOLS with asymptotic confidence interval (ACI) and sandwich confidence interval (SCI), a Monte-Carlo simulation is conducted to evaluate the performance of IOLS for comparison. The estimated coverage probability ( ) and average lengths ( ) will be used as performance criteria. The simulation study indicates that when reliability ratio ( ) less than 0.3 ( ),  of three methods are not close to specified confidence coefficient. For ,  of IOLS method is quite close to specified confidence coefficient and of IOLS method is the shortest. While ,  of SCI method is quite close to specified confidence coefficient and  of SCI method is the shortest.


Keywords :  confidence interval, regression coefficient, errors in variables

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