Bootstrap study to estimate linear regression parameter (Application in the study on the effect of oral hygiene on dental caries)

Background: Bootstrap is a computer simulation-based method that provides estimation accuracy in estimating inferential statistical parameters. Purpose: This article describes a research using secondary data (n = 30) aimed to elucidate bootstrap method as the estimator of linear regression test based on the computer programs MINITAB 13, SPSS 13, and MacroMINITAB. Methods: Bootstrap regression methods determine β̂ and Ŷ value from OLS (ordinary least square), i i i Y Y ˆ − = ε value, determine how many repetition for bootstrap (B), take n sample by replacement from i ε to ) (i ε , ) ( ˆ i i i Y Y ε + = value, β̂ value from sample bootstrap at i vector. If the amount of repetition less than, B a recalculation should be back to take n sample by using replacement from i ε . Otherwise, determine β̂ from “bootstrap” methods as the average β̂ value from the result of B times sample taken. Result: The result has similar result compared to linear regression equation with OLS method (α = 5%). The resulting regression equation for caries was = 1.90 + 2.02 (OHI-S), indicating that every one increase of OHI-S unit will result in caries increase of 2.02 units. Conclusion: This was conducted with B as many as 10,500 with 10 times iterations.