What effect does re-expressing data usually have on regression analysis?

Re-expressing data typically involves applying a mathematical transformation to the original values, such as taking the logarithm, square root, or reciprocal. This process is used primarily to address certain statistical issues that can arise in regression analysis, one of the most important being the stabilization of variance.

When the variance of the residuals (the differences between observed and predicted values) changes with the level of the independent variable, it violates one of the key assumptions of linear regression, known as homoscedasticity. By re-expressing the data, one can often achieve a more consistent variance across different levels of the independent variable, thus making the assumptions of linear regression more valid and the model more reliable.

This transformation can make the statistical relationships clearer, improve the model fit, and enhance predictive capabilities by ensuring the variance is stable across the range of data. Therefore, the effect of re-expressing data in regression analysis is most commonly associated with stabilizing the variance, which leads to improved interpretability and better statistical inference.