Explain the correlation of the data points to the equations shown in Figure 4.3

Correlation is a technique for investigating the relationship between two quantitative, continuous variables, for example, age and blood pressure. Pearson’s correlation coefficient (r) is a measure of the strength of the association between the two variables.

The first step in studying the relationship between two continuous variables is to draw a scatter plot of the variables to check for linearity. The correlation coefficient should not be calculated if the relationship is not linear. For correlation only purposes, it does not really matter on which axis the variables are plotted. However, conventionally, the independent (or explanatory) variable is plotted on the x-axis (horizontally) and the dependent (or response) variable is plotted on the y-axis (vertically).

Additionally, the nearer the scatter of points is to a straight line, the higher the strength of association between the variables. Also, it does not matter what measurement units are used.

Values of Pearson’s correlation coefficient

Pearson’s correlation coefficient (r) for continuous (interval level) data ranges from -1 to +1:

Positive correlation indicates that both variables increase or decrease together. Whereas negative correlation indicates that as one variable increases, so the other decreases, and vice versa.