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| Implementation of the BOX-COX transformation in linear regression with application condition violations |
| Chen Zicong1, Chen Hui2, Zhang Jinxin1 |
1 School of Public Health, Sun Yat-sen University, Guangzhou 510080, China;
2 Zhongshan Ophthalmic Center, Sun Yat-sen University |
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Abstract Objective When the application conditions of linear regression are violated, trying to implement the BOX-COX transformation can improve the application effect. This paper introduces the transformation process, which provides a reference for researchers to applying linear regression correctly. Methods The application steps and key points of the BOX-COX transformation were presented. SAS program was utilized to implement data transformation and regression diagnosis in the practical example. Results Before transformation, P value of the normality test was 0.016 and DW statistic was 2.547. Moreover, the distribution of residual plots was not uniform. After proper BOX-COX transformation, P value of the normality test was 0.669 and DW statistic was 2.193. Also, the distribution of residual plots became uniform. These indicated the transformed data basically satisfied the application conditions. Conclusion When the application conditions of linear regression are violated, BOX-COX transformation, while selecting appropriate parameters, can systematically, conveniently and effectively improve the distribution characteristics of residuals, so as to guarantee the correct application of regression analysis.
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Received: 06 November 2015
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