Final answer:
The influence of a data point on an ANOVA model is determined by examining the residuals, which measure the difference between observed and predicted values. Significant changes in the slope of the regression line after removing a point can indicate an influential point, as opposed to a mere outlier.
Step-by-step explanation:
In an ANOVA, the influence of a data point on the model is often measured by examining the residuals. A residual is the difference between the observed value and the predicted value given by the model. To determine if a data point is having an undue influence, you can remove it and see if there is a significant change in the slope of the regression line. This process helps to identify whether the point is an influential point or just an outlier. Influential points can significantly affect regression results, whereas outliers may not have a substantial impact on the model.
When discussing the regression line, the slope indicates the rate of change of the dependent variable (y) as the independent variable (x) increases. The y-intercept is the predicted value of y when x is zero. The fit of the regression line to the data is usually assessed using the correlation coefficient, r, and the standard deviation of the residuals. Finally, an influential point is typically distinguished from an outlier by its impact on the slope of the regression line and the overall fit of the model.