Final answer:
A line of best fit should not be drawn if it is significantly influenced by an outlier, which can be identified as a data point that lies more than two standard deviations from the line. Omitting the outlier often results in a line that more closely models the majority of the data by minimizing the residuals.
Step-by-step explanation:
When determining which line of best fit should not have been drawn, one must evaluate the scatter plot and the associated calculations. The line of best fit should be drawn in such a way that it minimizes the residuals, which are the differences between the observed values and the values predicted by the line. If a data point, such as an outlier, significantly deviates from the rest of the data and influences the line of best fit, leading to a line that does not well represent the spread of the data, it should not be included.
The implication of omitting the influential point is that the resulting line of best fit more closely models the bulk of the data since it has less deviation from the line. Outliers can affect the best-fit line significantly; if a data point is more than two standard deviations away from the line, it could skew the results and should hence be considered in the fitness of the line.
In light of the provided information, the correct answer would regard the line that takes into account the outlier. If this line deviates significantly from the majority of the data points, resulting in a higher sum of squared residuals compared to a line that excludes the outlier, then it should not have been drawn. An accurate line of best fit reflects the general trend of the data, excluding anomalous points that distort this trend.