Final answer:
The correct answer is C. Residuals should show no pattern around the horizontal axis, indicating that the residuals are independent, which is necessary for linear regression validity.
Step-by-step explanation:
C. Residuals should show no pattern around the horizontal axis,When plotting the residuals over time to look for correlated observations, if there is no violation of the independence assumption, you would see no pattern around the horizontal axis, meaning that the residuals would be randomly distributed. This random distribution indicates that the residuals are independent of each other, which is a crucial assumption for linear regression models to provide reliable results. The correct answer would be C. The residuals should show no pattern around the horizontal axis.
When assessing the appropriateness of a linear regression model, not only do you need to consider the residuals but also examine a scatter plot to see if a linear relationship exists between the independent (x) and dependent (y) variables.When plotting the residuals sequentially over time to look for correlated observations, if there is no violation, you would expect to see the residuals showing no pattern around the horizontal axis. This means that the residuals should be randomly scattered around the horizontal axis with no discernible pattern or trend.