Question

Twenty pairs of measurements were taken at random to estimate the relation between variables X and Y. A least-squares line was fitresidual plot is shown.Which of the following conclusions is appropriate?A. A line is an appropriate model to describe the relation between X and Y.B. A line is not an appropriate model to describe the relation between X and Y.avious QuestionC. The assumption of the Law of Averages has been violated.D. The variables X and Y are not related at all.E. There is not enough information about the variables X and Y to form a conclusion.

Answer 1

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

Explanation:

Answer 2

Given that twenty pairs of measurements were taken at random to estimate the relation between variables X and Y, you need to remember that, by definition:

`Residual=Observed\text{ }Values-Predicted\text{ }Values`

You can identify that the residual plot has a pattern that looks like a parabola.

By definition, when the pattern of a residual plot has a clear pattern, then a line is not an appropriate model to fit the relation between the variables.

Therefore, in this case, the model is a non-linear model.

Hence, the answer is: Option B.