September 13, 2023

Heteroscedasticity is important to ensure that the assumptions of the model are met and that the results are valid. Breusch-Pagan test is used to test heteroscedasticity analytically. The Breusch–Pagan test, developed in 1979 by Trevor Breusch and Adrian Pagan. There are a couple of variants of the Breusch-Pagan test. It uses the residuals from the original linear regression of %diabetes against %inactivity. Calculate Pearson’s R-Squared  and then the calculate the p-value. A p-value is a peculiar value which is a method to assess whether the results of an experiment or study are statistically significant or whether they could have occurred by chance. We need to see the p-value is as large as n  where n = 1370 which is the number of %inactivity data points for a chi-squared distribution with degree of freedom. Typically, p-value is very small such as 0.05, it means it has strong evidence against the null hypothesis. In these types of cases, they choose to reject the null hypothesis that the original linear model is homoscedastic.

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