A scatter diagram is given with one of the points labeled ʺA.ʺ In addition, there are two least -squares regression lines
drawn. The solid line excludes the point A. The dashed line includes the point A. Based on the graph, is the point A
influential
-An influential observation is an observation that significantly affects the value of the
A) the slope of the least squares regression line.
B) the mean of the response variable.
C) the median of the predictor variable.
D) the median of the response variable.

Question

Quizplus · Accepted Answer

An influential observation significantly affects the slope of the least squares regression line. If including or excluding a point (like point A) changes the slope of the regression line (as indicated by the presence of two different lines, one solid and one dashed), it demonstrates that the point is influential. Influential points can significantly alter the direction and steepness of the regression line, which is a measure of the relationship between the predictor and response variables. Influential points do not directly affect the mean or median of the response or predictor variables in the context of regression analysis; their primary impact is on the regression line's parameters.

A Scatter Diagram Is Given with One of the Points