The correlation coefficient measures the robustness of the relationship between two variables. Pearson's correlation coefficient is one of the most commonly used correlation coefficient and measures the linear relationship between two variables. The value of the correlation coefficient, denoted as r, ranges from -1 to +1, which gives the strength of the relationship and whether the relationship is negative or positive. When the value of r is greater than zero, it is a positive relationship; when the value is less than zero, it is a negative relationship. A value of zero indicates that there is no relationship between the two variables.
If the correlation coefficient of two variables is zero, it signifies that there is no linear relationship between the variables. However, this is only for a linear relationship; it is possible that the variables have a strong curvilinear relationship. When the value of r is close to zero, generally between -0.1 and +0.1, the variables are said to have no linear relationship or a very weak linear relationship. For example, suppose the prices of coffee and of computers are observed and found to have a correlation of +.0008,; this means that there is no correlation. or relationship, between the two variables.
A positive correlation. when r is greater than 0, signifies that both variables move in the same direction. When r is +1,
it signifies that the two variables being compared have a perfect positive relationship; when one variable moves higher or lower, the other variable moves in the same direction with the same magnitude. The closer the value of r is to +1, the stronger the linear relationship. For example, suppose the value of oil prices are directly related to the prices of airplane tickets, with a correlation coefficient of +0.8. The relationship between oil prices and airfares has a very strong positive correlation, since the value is close to +1. So if the price of oil decreases, airfares follow in tandem. If the price of oil increases, so does the prices of airplane tickets.
A negative correlation. when r is less than 0, indicates that both variables move in the opposite direction. When r is -1, the relationship is said to be perfectly negative correlated; in short, if one variable increases, the other variable decreases with the same magnitude, and vice versa. For example, suppose a study is conducted to assess the relationship between outside temperature and heating bills. The study concludes that there is a negative correlation between the prices of heating bills and the outdoor temperature. The correlation coefficient is calculated to be -0.96. This strong negative correlation signifies that as the temperature decreases outside, the prices of heating bills increase and vice versa.