Question at position 6 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.Exercise hours do not predict happiness scores.Higher exercise hours cause lower happiness scores.Happiness scores are independent of exercise hours.

Question

Question at position 6 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.Exercise hours do not predict happiness scores.Higher exercise hours cause lower happiness scores.Happiness scores are independent of exercise hours.

BlackTom AI · Accepted Answer

Starting with the core idea: a positive correlation between daily exercise and happiness scores means that as one variable increases, the other tends to increase as well. With that in mind, we evaluate each option.
Option 1: 'Higher exercise hours are associated with higher happiness scores.' This aligns with the meaning of a positive correlation: a trend where higher values of one variable accompany higher values of the other. It correctly captures the observed association.
Option 2: 'Exercise hours do not predict happiness scores.' This statement would imply no relationship or a zero correlation. A significant positive correlation contradicts this, indicating that exercise hours do relate to happiness scores in a systematic way.
Option 3: 'Higher exercise hours cause lower happiness scores.' This describes a negative or inverse relationship, not a positive one. It misstates both the direction and the nature of the association suggested by the data.
Option 4: 'Happiness scores are independent of exercise hours.' Declaring independence means no association at all. A significant positive correlation directly contradicts the notion of independence, since independence would imply no predictable change in happiness with changes in exercise.
In summary, the first option correctly characterizes the identified relationship, while the other options describe relationships or lack thereof that are inconsistent with a significant positive correlation. The interpretation hinges on understanding correlation as a mutual association where increases in one variable tend to accompany increases in the other, rather than implying causation or no relationship.

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