A scatter plot is a graphical tool that shows the relationship between two continuous variables by plotting data points at their corresponding values on the x-axis and y-axis1.
To interpret a scatter plot, we need to look at the direction, strength, and shape of the relationship between the variables2.
The direction of the relationship indicates whether the variables tend to increase or decrease together (positive correlation) or in opposite directions (negative correlation).
The strength of the relationship indicates how closely the data points cluster around a line or curve that best fits the data. A common measure of the strength of the linear relationship is the correlation coefficient ®, which ranges from -1 to 1. The closer the absolute value of R is to 1, the stronger the linear relationship2.
The shape of the relationship indicates whether the data points follow a straight line (linear relationship) or a curved pattern (nonlinear relationship).
Based on these criteria, we can analyze the scatter plots for Setting 1 and Setting 2 as follows:
Setting 1: The scatter plot shows a clear upward trend, indicating a positive correlation between complication rate and time to positive outcome. Thedata points are tightly clustered around a line, indicating a strong linear relationship. The R^2 value of 0.9533 on the plot is close to 1, which means that the linear model explains 95.33% of the variation in the complication rate. Therefore, we can conclude that Setting 1 has a strong positive correlation between complication rate and time to positive outcome.
Setting 2: The scatter plot shows a scattered pattern, indicating a weak or no correlation between complication rate and time to positive outcome. The data points are widely spread around a line, indicating a weak linear relationship. The R^2 value of 0.4923 on the plot is far from 1, which means that the linear model explains only 49.23% of the variation in the complication rate. Therefore, we cannot conclude that Setting 2 has a significant correlation between complication rate and time to positive outcome, or that complication rates are causing longer time to positive outcome at setting 2.
[References: 1: 8.8 Scatter Plots, Correlation, and Regression Lines 2: Scatterplots: Using, Examples, and Interpreting, , , , , , ]
