What does a perfect negative correlation look like?

A perfect negative correlation looks like a straight line sloping downwards on a scatter plot.

In more detail, a perfect negative correlation means that as one variable increases, the other variable decreases at a consistent rate. This relationship is represented by a correlation coefficient of -1. On a scatter plot, you would see all the data points forming a straight line that goes from the top left to the bottom right. For example, if you were plotting the number of hours studied against the number of mistakes made on a test, a perfect negative correlation would show that more hours of study consistently lead to fewer mistakes.

In mathematical terms, if you have two variables, X and Y, a perfect negative correlation means that for every unit increase in X, there is a proportional unit decrease in Y. This relationship can be described by the equation Y = -mX + c, where m is the slope of the line and c is the Y-intercept. The negative sign indicates the inverse relationship between the two variables.

Understanding perfect negative correlation is important because it helps you predict one variable based on the other. For instance, if you know that there is a perfect negative correlation between the amount of exercise and body weight, you can predict that increasing exercise will lead to a decrease in body weight. This concept is widely used in fields like economics, biology, and social sciences to analyse and interpret data.