Question

fifteen pairs of measurements were taken at random to estimate the relation between variables x and y. a least-squares line was fitted to the collected data. this resulting residual plot is shown
which of the following conclusions is appropriate?
a line is an appropriate model to describe the relation between x and y
a line is not an appropriate model to describe the relation between x and y
the assumption of the law of averages has been violated
the variables x and y are not related at all

Explanation:

A residual plot for a valid linear model should show residuals randomly scattered around 0 with no clear pattern. This plot has a curved, U-shaped pattern, which indicates that a linear model fails to capture the relationship between X and Y. The Law of Averages is not relevant here, and the pattern shows there is a relationship, just not linear.

Answer:

B. A line is not an appropriate model to describe the relation between X and Y