Which of the following is true about Pearson residuals?

Pearson residuals are a crucial tool in statistical modeling, especially in the context of generalized linear models (GLMs). The correct understanding is that Pearson residuals can indeed indicate unusual observations in the dataset. They are calculated as the difference between the observed values and the predicted values, standardized by the estimated standard deviation. Essentially, they provide insight into how far an individual observation deviates from what the model predicts, adjusted for the model's variance.

When examining the residuals, particularly Pearson residuals, one can identify outliers or anomalous data points that may have a significant influence on the model’s estimates. Observations with large absolute values for Pearson residuals suggest that those points do not align well with the projected outcomes of the model, contributing to the idea that these observations could be unusual or problematic.

In contrast, the other choices present inaccurate or incomplete views. While Pearson residuals can be associated with model improvement, this is not their primary role. They do have a significant role in assessing model fit, as they help evaluate how well the model captures the data patterns. Furthermore, Pearson residuals are not restricted to linear regression models; they are widely applicable to a variety of model types, particularly those that fall under the umbrella of generalized linear models