Regression Lines

A regression line is a line drawn on a scatterplot that describes the linear relationship between that scatterplots explanatory and response variables. The line is used to predict a value of the response variable for a given value of the explanatory variable.

A regression line is drawn in red on the scatterplot below.



Influential Observations
An influential observation is an outlier that has a great influence on a regression line.
A regression line is made in a way that seeks to minimise the total distance between itself the points on the scatterplot. Because of this, the presence of large outliers can significantly affect its properties. To find out if an observation is influential, the regression line can be redrawn with that observation excluded. If there is a significant difference from the original line then the observation is influential.