What is an observation called that has a strong influence on the outcome of regression results?

An influential observation is a data point that significantly affects the outcome of a regression analysis. These points can sway the estimates of regression coefficients, potentially leading to different conclusions compared to analyses without them. An influential observation is often identified through its leverage and the distance of its response from the predicted line.

When these observations have high leverage or contribute disproportionately to the error, they can drastically alter the slope of the regression line, the intercept, and consequently the overall fit of the model. Detecting and assessing influential observations is crucial in regression analysis, as they can indicate potential data errors, unusual variability, or noteworthy trends that warrant further investigation.

In contrast, an outlier refers more broadly to a data point that lies outside the overall pattern of distribution, not necessarily implying that it will have a strong effect on the regression results. A residual is the difference between the observed value and the value predicted by the regression model, which doesn't directly indicate influence. Lastly, a variable is a feature or quantitative measure used in the analysis, without necessarily implying its effect on outcomes.