Question

Consider the following scatterplot of amounts of co (carbon monoxide) and nox (nitrogen oxide) in grams per mile driven in the exhausts of cars. The least-squares regression line has been drawn in the plot. What does the point indicated by the open circle in the scatterplot represent?

1) An outlier
2) A missing data point
3) A predicted value
4) Cannot be determined from the given information

Answer 1

The open circle in the scatterplot signifies an outlier, which is a data point significantly distant from the least-squares regression line, typically more than two standard deviations away.

Step-by-step explanation:

The point indicated by the open circle in the scatterplot represents an outlier. An outlier is an observation that lies at an abnormal distance from other values in a random sample from a population, specifically if it is more than two standard deviations away from the least-squares regression line. In terms of residuals, or the differences between the observed values and the values predicted by the regression line, anything beyond two standard deviations is considered significant. In a scatterplot, outliers can be identified visually by the data point's distance from the regression line, or numerically by comparing the residual to twice the standard deviation of the residuals.