Question

Which two sentences about inferences based on numeric variables are true? A strong positive or negative correlation can be used to prove a causal relationship, while the absence of correlation can be used to rule out a causal relationship. The absence of correlation can be used to rule out a causal relationship, but the presence of a strong positive or negative correlation does not prove a causal relationship. Strong correlations between two variables are sometimes explained by the influence of a third lurking variable that has a causal relationship with both variables. If a variable is known to be affected by multiple causes, its strong positive or negative correlations with other variables are likely to be spurious.

Answer 1

The true statements about inferences based on numeric variables are that the absence of correlation can suggest no causal relationship, while a strong correlation does not prove causation, and strong correlations could be due to a lurking third variable.

Step-by-step explanation:

Among the statements provided about inferences based on numeric variables, the following two sentences are true: 'The absence of correlation can be used to rule out a causal relationship, but the presence of a strong positive or negative correlation does not prove a causal relationship.' and 'Strong correlations between two variables are sometimes explained by the influence of a third lurking variable that has a causal relationship with both variables.' These statements are correct because a correlation, whether strong or not, only indicates that there is a relationship between two variables, not that one causes the other. This difference between correlation and causation is crucial in statistics and scientific research.

Answer 2

Answer: The absence of correlation can be used to rule out a causal relationship, but the presence of a strong positive or negative correlation does not prove a causal relationship.

Step-by-step explanation:

When there is a correlation between two events, it means that they occur in a certain way in regards to each other. This does not always mean that one causes the other however as it could simply be coincidence.

On the other hand, if there is no correlation whatsoever, then there is no causal relationship because if one of the events causes the other, it would have to be correlated with it.