Residual Analysis in Simple Linear Regression: A Practical Application with the Jarque-Bera Test

Residual Analysis in Simple Linear Regression: A Practical Application with the Jarque-Bera Test

Siddamsetty Upendra1, Dr. R. Abbaiah2, Dr. P. Balasiddamuni3,  Dr. K. Murali4

1,2,3,4 Department of Statistics, S V University, Tirupathi, India

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Abstract- This study provides a practical guide to residual analysis in ordinary linear regression, a basic statistical technique. Explains how to calculate and interpret residuals, which play a key role in assessing model validity. The study then focuses on the Jarque-Bera test, a diagnostic tool used to assess the normality of residuals. Through a step-by-step example, we show how to calculate the skewness and kurtosis of the residuals, and then calculate the Jarque-Bera test statistic. We highlight the importance of this test in determining whether residuals obey a normal distribution, helping researchers make reliable statistical inferences. This practical guide helps readers understand the importance of residual analysis in building robust regression models.

Keywords:       Residual analysis, simple linear regression, model assumptions, Ordinary Least Squares, OLS estimation, Jarque-Bera test, normality, validation, practical example.