Please give your best opinion as needed.
In many business and economics applications, we may observe highly
correlated variables when each pair of observations corresponds to a
particular time period. For example, we would expect a high correlation
between average annual wages and the U.S. gross national product (GNP) when
measured over time.
a. Since wages may be a good predictor of U.S. GNP, is it also true that an increase in wages causes an increase in U.S. GNP?
b. Explain your answer in part (a) above.
c. Describe a different example of where the independent variable, while highly correlated to the dependent variable, does not cause the dependent variable to change directly.
d. Discuss the differences and relationship between correlation and determination as it applies to linear regression analysis.
This example demonstrates that correlation and causation are not the same thing in the realm of statistics. In other words, although two variables may be strongly correlated, we cannot conclude that one variable necessarily can be derived from the other one.