### Bootstrapping Residuals to Estimate the Standard Error of Simple Linear Regression Coefficients

#### Abstract

Regression models are the statistical methods that widely used in many fields. The models allow relatively simple analysis of complicated situations. The aim of the regression models is to analyze the relationship between the predictor and response. In order to do that, we have to estimate the regression coefficient. In case of simple linear regression, the method to estimate the regression coefficient is either least square method or maximum likelihood estimation. Also, the standard error of the regression coefficient is being estimated. In this paper, we apply the bootstrap method to estimate the standard error of the regression coefficient. We compare the result of the bootstrapping method with the least square method. From this study, we know that the standard error estimation value of regression model using the bootstrap method is close to the value if we use the least square method. So we can say that the bootstrap method can be used to estimate the standard error of another regression models coefficient which does not have the closed-form formula

#### Keywords

bootstrap; simple linear regression; least square; residuals; standard error

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#### References

Chatterjee, S., Price, B. 1977. Regression Analysis by Example. John Wiley & Sons, Inc. New York 

Draper, N., Smith, H. 1992. Analisis Regresi Terapan Edisi Kedua. PT Gramedia Pustaka Utama. Jakarta

Effron, B., Tibshirani, R.J. 1993. An Introduction to the Bootstrap. Chapman & Hall. London

Kreiss, J. P., Paparoditis, E. 2015. Bootstrapping Locally Stationary Processes. Journal of The Royal Statistical Society. B, 77, 267-290

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