Week 4 Discussion

Correlation

Two variables are said to be in correlation if a change in one of the variables results in a change in the

other variable. Correlation analysis is used to determine the degree of this association between two

variables. For example, portfolio managers can use a correlation analysis to measure the degree of

relationship between the returns of two stocks. However, correlation analysis cannot measure a nonlinear relationship between two variables, if such a nonlinear relationship exists.

The Pearson correlation coef�cient, also known as the sample correlation coef�cient, is an important

component of correlation analysis. The sample correlation coef�cient can range from -1.0 to +1.0. It is

typically rare for the value to be exactly equal to -1.0, 0, or +1.0. However, these values represent

speci�c meanings that are worthy of discussion.

-1

A correlation coef�cient that is equal to -1.0 indicates a perfectly negative relationship between two

variables. For example, variables representing the price and demands of a product will have negative

correlation. For most products, when the price of the product goes up, the demand for the product

goes down.

0

A correlation coef�cient that is equal to 0 indicates that there is no linear relationship between two

variables. A change in one variable is predicted to have no impact on the other variable.

+1

A correlation coef�cient that is equal to +1.0 indicates a perfectly positive relationship between two

variables. For example, variables representing the price and supply of a product will have positive

correlation. If supply can be adjusted, for most products, when the price of the product goes up, the

supply that will be provided to the marketplace goes up.

There is a t-test that can be used to determine if a correlation coef�cient is signi�cantly different from zero. Thus, if this test shows that there is evidence that the correlation coef�cient is signi�cantly

different from zero, the research can conclude that there is a statistically signi�cant correlation (either

positive or negative) between the two variables.