Final answer:
A residual plot featuring a random scatter of points suggests data homoscedasticity and appropriateness for linear regression. A plot with clear patterns, such as curvature, implies a nonlinear relationship, making option C ('The data may have a nonlinear relationship') the correct choice.
Step-by-step explanation:
When analyzing a residual plot, it's critical to discern the patterns it reveals about the original scatterplot from which the residuals were calculated. The residual plot can tell us whether the data was homoscedastic, which means that the variances along the line of best fit remain similar as we move along the x-axis, or if there is heteroscedasticity, where the variances differ at different points along the x-axis.
If the residual plot shows a random scatter of points without any discernible pattern, this suggests that the original data is homoscedastic and that a linear regression model may be appropriate. On the other hand, if the residuals have a distinct pattern, such as a curvature or fan shape, this implies nonlinear relationships or heteroscedasticity in the original scatterplot, thus indicating that a linear model might not be the best fit for the data.
An ideal residual plot that would support a perfect linear relationship (option D) would exhibit no pattern at all, with residuals randomly dispersed around the horizontal axis (the line where the residual is zero). If residuals show a strong pattern, this would not support a perfectly linear relationship.
Therefore, based on the option that the residual plot demonstrates a pattern, we can conclude that option C ('The data may have a nonlinear relationship') is the most likely correct choice.