* 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. The data 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