Example 1: Scatter DiagramSolutiona) The values in the table make ordered pairs. To make the scatter diagram, scan the data and choose an appropriate scale for each axis. Phosphorous Reduction (100 mg/l) Figure 9.1 The line segment shows the basic trend.
Scatter Diagrams and Linear Correlation • If the points of a scatter diagram are located so that NO line is realistically a “good” fit, then we say that the points possess no linear correlation. (a) (b) Scatter Diagrams with No Linear Correlation Figure 9.2
Example: Computing r• Sand driven by wind creates large, beautiful dunes at the Great Sand Dunes National Monument, Colorado. Of course, the same natural forces also create large dunes in the Great Sahara and Arabia. Is there a linear correlation between wind velocity and sand drift rate? Let x be a random variable representing wind velocity (in 10 cm/sec) and let y be a random variable representing drift rate of sand (in 100 gm/cm/sec). A test site at the Great Sand Dunes National Monument gave the following information about x and y (Reference: Hydrologic, Geologic, and Biologic Research at Great Sand Dunes National Monument, Proceedings of the National Park Service Research Symposium).
Causation• The correlation coefficient is a mathematical tool for measuring the strength of a linear relationship between two variables. • It makes no implication about cause or effect.• The fact that two variables tend to increase or decrease together does not mean that a change in one is causing a change in the other.• A strong correlation between x and y is sometimes due to other (either known or unknown) variables. Such variables are called lurking variables.