The value for the correlation coefficient can be used to determine the strength of the relationship between the two variables represented in the data.
In general, when the variables increase together, we can say they have a positive relationship. If an increase in one variable’s data tends to be paired with a decrease in the other variable’s data, the variables have a negative relationship. When the data is tightly clustered around the best fit line, we say there is a strong relationship. When the data is loosely spread around the best fit line, we say there is a weak relationship.
A correlation coefficient with a value near 1 suggests a strong, positive relationship between the variables. This means that most of the data tends to be tightly clustered around a line and that when one of the variables increases in value, the other does as well. The number of schools in a community and the population of the community is an example of variables that have a strong, positive correlation. When there is a large population, there is usually a large number of schools, and small communities tend to have fewer schools, so the correlation is positive. These variables are closely tied together, so the correlation is strong.
Similarly, a correlation coefficient near -1 suggests a strong, negative relationship between the variables. Again, most of the data tend to be tightly clustered around a line, but now, when one value increases, the other decreases. The variables time since leaving home and the distance left to reach school have a strong, negative correlation. As the travel time increases, the distance to school tends to decrease, so this is a negative correlation. The variables are again closely, linearly related, so this is a strong correlation.
Weaker correlations mean there may be other reasons the data is variable other than the connection between the two variables. For example, variables number of pets and number of siblings have a weak correlation. There may be some relationship, but there are many factors that account for the variability in the number of pets other than the number of siblings.
The context of the situation should be considered when determining whether the correlation value is strong or weak. In physics, where things are measured with precise instruments, a correlation coefficient of 0.8 may not be considered strong. In social sciences, where data is collected through surveys, a correlation coefficient of 0.8 may be very strong.
