Influential observations are characterized by which of the following?

Influential observations are those data points that significantly impact the results of a statistical analysis, particularly in regression analysis. When these observations are present in a dataset, they can disproportionately affect the estimation of parameters, the fit of the model, and consequently the conclusions drawn from the analysis. For example, if an influential observation lies far away from the rest of the data points, it can skew the regression line, altering the slope and intercept in a way that may not accurately reflect the overall trend of the data.

Given this definition, it is clear why the option mentioning a strong impact on results is the correct one. Influential observations serve as crucial indicators that analysts must pay attention to, as their presence can provide insights into variability in the data or possible errors in measurement. Recognizing and investigating these observations is vital for ensuring robust statistical analyses.