![]() 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. Using the scatterplot, comment on the relationship between the two variables. This relationship is monotonic, but not linear. Is the relationship weak, moderate, or strong. Plot 5 shows both variables increasing concurrently, but not at the same rate. 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. A weak positive correlation graph is where the line is far from every data point, and the line has a positive slope. This relationship illustrates why it is important to plot the data in order to explore any relationships that might exist. A strong positive correlation graph is where the line touches or is very close to every data point, and the line has a positive slope. However, because the relationship is not linear, the Pearson correlation coefficient is only +0.244. b) If the correlation is positive or negative, determine if it is a strong or weak correlation. Here we have that increase in X is associated with decrease in Y. NOTES: Scatter Plots and Correlation scatter plot is often. Negative correlation is a relationship between 2 variables ( X and Y ) : one increases as the other decreases. ![]() Plot 4 shows a strong relationship between two variables. There can be: positive correlation, negative correlation, equal correlation or no correlation. 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. The example generated by XmdvTool shows a 4x4 scatter plot matrix of the variables medhvalue. Scatter plot matrix: Given a set of variables, the scatter plot matrix contains all the pair-wise scatter plots of the variables on a single page in a matrix format. They do not fall close to the line indicating a very weak relationship if one exists. Weak linear correlation: The closer the number is to 0, the weaker the correlation. If the variables are correlated, the points will fall along a line or curve. The data points in Plot 3 appear to be randomly distributed. We know that the correlation is a statistical measure of the relationship between the two variables’ relative movements.
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