Transforming variables can help meet assumptions such as linearity and homoscedasticity from "summary" of Introduction to Econometrics by Christopher Dougherty
When fitting a linear regression model, it is crucial to ensure that the underlying assumptions are met for the model to be valid. Two key assumptions are linearity and homoscedasticity. Linearity assumes that the relationship between the independent and dependent variables is linear, while homoscedasticity assumes that the variance of the errors is constant across all levels of the independent variables. However, in practice, the relationship between variables may not always be linear or the variance of the errors may not be constant. This is where transforming variables comes into play. By transforming variables, we can potentially meet the assumptions of linearity and homoscedasticity. For example, if the relationship between the variables appears to be curvilinear, we can use transformations such as taking the logarithm or the square root of the variables to make the relationship more linear. This transformation can help capture the non-linear relationship in a linear model, thus meeting the assumption of linearity. Similarly, if the variance of the errors is not constant across different levels of the independent variable, we can use transformations such as taking the square root or the reciprocal of the dependent variable. This transformation can help stabilize the variance of the errors and meet the assumption of homoscedasticity.- Transforming variables can be a useful tool in econometrics to ensure that the assumptions of linearity and homoscedasticity are met, thereby ensuring the validity of the regression model. By carefully choosing appropriate transformations, we can improve the model's accuracy and reliability, leading to more robust econometric analysis.
