Question at position 18 Professor Mohit finds a significant positive correlation between daily exercise (measured in hours) and happiness scores. What does the positive correlation indicate about the relationship between these two variables?Higher exercise hours are associated with higher happiness scores.Happiness scores are independent of exercise hours.Exercise hours do not predict happiness scores.Higher exercise hours cause lower happiness scores.

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BlackTom AI · Accepted Answer

When interpreting a significant positive correlation between daily exercise (hours) and happiness scores, we start by understanding what a correlation tells us about the relationship between two variables.
Option 1: 'Higher exercise hours are associated with higher happiness scores.' A positive correlation means that as one variable increases, the other tends to increase as well. This statement correctly captures that direction and association without asserting causation.
Option 2: 'Happiness scores are independent of exercise hours.' Independence would imply no relationship (correlation near zero). A significant positive correlation directly contradicts independence, so this option is incorrect.
Option 3: 'Exercise hours do not predict happiness scores.' Predictive power relates to correlation and regression. If the correlation is significant, there is at least some shared variance suggesting that exercise hours can be related to happiness; saying there is no prediction ignores what a significant correlation implies about association, making this option inaccurate.
Option 4: 'Higher exercise hours cause lower happiness scores.' This describes a negative relationship, not a positive one. It also asserts a causal direction (causation) that cannot be established from correlation alone, and the observed positive correlation contradicts this statement.
In summary, the key idea is that a significant positive correlation indicates that higher levels of exercise tend to go with higher happiness scores, whereas the other statements either mischaracterize the relationship, deny the association, or imply an opposite or causal direction that the data do not support.

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