Final answer:
You can calculate a regression line for data that form a straight line or have a high correlation coefficient, but for curved data or data with low correlation coefficient, other models might be more suitable.
Step-by-step explanation:
When determining whether a regression line can be reasonably determined for a set of data points, one should consider the pattern that the data exhibits.
For a set of data points that form a straight line (option 1), it is most suitable to calculate a linear regression line, as the data already exhibit a linear relationship. For data that form a curve (option 2), while a regression line can still be calculated, it might not be the best model, and other types of regression such as polynomial regression might be more appropriate.
For data points that have a high correlation coefficient (option 3), finding a regression line is typically reasonable because a high correlation coefficient suggests a strong linear relationship between the variables. However, for data points with a low correlation coefficient (option 4), while a regression line can still be determined, it may not model the relationship well, and the predictive power of such a line would be weak.
Ultimately, apart from computational suitability, the choice to model data with a regression line also depends on the significance of the correlation coefficient and the visual pattern observed in a scatter plot. Even with a significant correlation coefficient, if the data visual suggests a non-linear relationship, other modeling approaches may be more appropriate.