Questions: An examination of data reveals a positive correlation between the demand for new homes and the price of lumber. Which of the following conclusions can be correctly inferred from the existence of this correlation? Why? 1) An increase in the demand for new homes causes an increase in the price of lumber. ii) The observed correlation is consistent with a theory that an increase in demand for new homes causes an increase in the price of lumber. Conclusion can be correctly inferred from the existence of this correlation because there is direct evidence of a causal relationship between the demand for new homes and the price of lumber.

Solution Steps

Correlation indicates a relationship between two variables, but it does not imply causation. In this case, the positive correlation between the demand for new homes and the price of lumber means that as one increases, the other tends to increase as well. However, this does not necessarily mean that one causes the other.

Conclusion 1 states that an increase in the demand for new homes causes an increase in the price of lumber. While this is a plausible explanation for the observed correlation, it cannot be definitively inferred from the correlation alone. There could be other factors at play, such as external economic conditions or supply chain issues, that influence both variables.

Conclusion ii states that the observed correlation is consistent with a theory that an increase in demand for new homes causes an increase in the price of lumber. This conclusion is more cautious and accurate because it acknowledges that the correlation supports the theory but does not assert causation. It aligns with the principle that correlation can be consistent with a causal relationship but does not prove it.

Conclusion \(\boxed{ii}\) can be correctly inferred from the existence of this correlation because there \(\boxed{is no}\) direct evidence of a causal relationship between the demand for new homes and the price of lumber.

Final Answer