Question

Correlation and Causality: What is meant by the statement that correlation does not imply causality? Part 2: Cause of Global Warming: If we find that there is a linear correlation between the concentration of carbon dioxide (CO2) in our atmosphere and the global temperature, does that indicate the changes in the concentration of carbon dioxide cause changes in the global temperature? Why or why not? Part 3: Application of concepts: Discuss and give at least one example of how you will use the information in chapter 10 in your area of study.

Answer 1

Correlation:

• By definition, measure Pearson's correlation coefficient quantifies the strength and direction of the linear relation between two continuous variables - here, the concentration of carbon dioxide (CO2) in our atmosphere and the global temperature.
• It ranges from -1 to 1, negative and positive values indicating a negative and positive linear relationship respectively.
• Values close to unity, depicts a strong linear relationship and those close to zero implies weak or no linear relationship.
• A significant linear relationship implies that there is a particular trend in the data, and the two variables tend to move together.

Suppose we find that the variables concentration of carbon dioxide (CO2) in our atmosphere (X,say) and the global temperature (Y,say) are significantly positively correlated: This shows that - As the concentration of carbon dioxide (CO2) in our atmosphere increases (decreases), the global temperature also increases (decreases). This correlation may also be interpreted as Y increases (decreases), X also increases (decreases); which hardly applies to the causal relationship that we expect.

Hence, the statement "there is a linear correlation between the concentration of carbon dioxide (CO2) in our atmosphere and the global temperature, indicates the changes in the concentration of carbon dioxide cause changes in the global te

mperature" cannot be proved simply using a measure of correlation. The reason's being:

• Since, in correlation, "change in X causes change in Y" is same as "change in Y causes change in X". However, this is not the case in causation where, "change in X causes change in Y" sounds meaningful whereas "change in Y causes change in X" does not.
• X and Y may be correlated but both are actually affected / caused by Z.
• Spurious correlation:

A commonly cited classic example would be a positive correlation between Sale of ice-cream and murder rates during summer. Here, the interpretation of this correlation makes little sence. Such correlations a just a mathematical relation / trend observed in values of any two set of numbers / variables, which in real world might make no sense.

Part 3: Suppose, we wish to establish a causal relationship between two variables say, No. of hours studied and GPA; we may first find out how the strongly the two variables are related and if we get the expected (say, strong positive relation) result, we may go further to test the causal relationship between the two.