Final answer:
C. The residuals should show no pattern around the horizontal axis. This indicates that the residuals are independent, which is a necessary condition for proper linear regression analysis. The assessment of scatter plots and the investigation of outliers are also important in evaluating the suitability of a linear regression model.
Step-by-step explanation:
When plotting residuals sequentially over time to look for correlated observations, if there is no violation of the independence assumption, then you would see that the residuals should show no pattern around the horizontal axis, which is option C. The absence of a pattern indicates that the residuals are indeed independent, which is a necessary condition for a proper linear regression analysis. If patterns or trends are observed, this might indicate autocorrelation or other violations of linear regression assumptions, suggesting the need for further analysis or different modeling approaches.
When analyzing the appropriateness of a linear regression model, it is essential to examine a scatter plot to identify any visible patterns. If the scatter plot shows a linear relationship with data points distributed randomly around the best-fit line and no apparent pattern, it indicates a potentially good linear regression model. On the other hand, if the scatter plot reveals a non-linear pattern, a curve may be more suitable than a straight line.
Overall, the sequential plot of residuals, the evaluation of scatter plots, and the investigation of potential outliers all play crucial roles in assessing the suitability of a linear regression model for a set of data.