Regression Line and Influential Clusters

Question

A researcher studying the relationship between weekly exercise hours and resting heart rate observes a tight cluster of data points. What would happen if a new cluster showing higher exercise hours and lower heart rates were added?

Accepted Answer

The regression line would shift to accommodate the new trend, likely resulting in a steeper negative slope and a modified intercept.

Answer

Only the variability within the new cluster would be affected, leaving the original regression line and its parameters unaltered by the addition of distinct data points.

Answer

The addition of the new cluster would have negligible effect on the overall regression line because the original cluster dominates the dataset.

Answer

The regression analysis would become invalid as the presence of two separate clusters inherently violates the assumptions of linear regression, leading to a complete breakdown of the model's predictive capacity in an unpredictable and erratic manner that defies standard statistical interpretation.