Positive non linear scatter plot7/2/2023 ![]() ![]() For example, the relationship shown in Plot 1 is both monotonic and linear. The Pearson correlation coefficient for these data is 0.843, but the Spearman correlation is higher, 0.948. This relationship is monotonic, but not linear. Plot 5 shows both variables increasing concurrently, but not at the same rate. When both variables increase or decrease concurrently and at a constant rate, a positive linear relationship exists. In a linear relationship, the variables move in the same direction at a constant rate. In a monotonic relationship, the variables tend to move in the same relative direction, but not necessarily at a constant rate. This relationship illustrates why it is important to plot the data in order to explore any relationships that might exist. One could consider transforming the variables for linearity (re-expression) or use non-linear regression. However, because the relationship is not linear, the Pearson correlation coefficient is only +0.244. These are clearly two non-linear relationships. A scatterplot in which the points do not have a linear trend (either positive or negative) is called a zero correlation or a near-zero correlation (see below). ![]() Plot 4 shows a strong relationship between two variables. This curved trend might be better modeled by a nonlinear function, such as a quadratic or cubic function, or be transformed to make it linear. ![]() If a relationship between two variables is not linear, the rate of increase or decrease can change as one variable changes, causing a "curved pattern" in the data. The Pearson correlation coefficient for this relationship is −0.253. In other words, when all the points on the scatter diagram tend to lie near a. They do not fall close to the line indicating a very weak relationship if one exists. Correlation is said to be non linear if the ratio of change is not constant. The data points in Plot 3 appear to be randomly distributed. ![]()
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