Question

Eighteen 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. The resulting residual plot is shown.

Which of the following conclusions is appropriate?

The assumption of the Law of Averages has been violated.
The variables X and Y are not related at all.
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.

Answer 1

Based on the information provided, the appropriate conclusion is that a line is an appropriate model to describe the relation between variables X and Y.

Explanation:

A residual plot is a useful tool for assessing the appropriateness of a linear model. In a residual plot, the residuals (the differences between the observed Y values and the predicted Y values from the fitted line) are plotted against the corresponding X values. If the residuals exhibit a random pattern with no clear trend or systematic deviation from zero, it indicates that the linear model is appropriate for describing the relationship between the variables.

In this case, if the residual plot shows a random scatter of points around the zero line, with no distinct pattern or trend, it suggests that the line fitted to the data is a good representation of the relationship between X and Y. This means that a line is an appropriate model to describe the relation between the variables.

It's important to note that this conclusion is based on the assumption that the least-squares line was fitted correctly to the collected data. Additionally, it's always a good idea to consider other factors, such as the context of the data and the specific goals of the analysis, before drawing final conclusions.