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AP Statistics/Unit 2: Exploring Two-Variable Data
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Regression Line and Influential Clusters

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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?

A

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

B

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.

C

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.

D

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

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