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(Chapter 8, STAT 1040)

Correlation

Scatter Diagrams

A scatter diagram or scatter plot shows the relationship between two variables. One variable is on the X axis, the other on the Y axis.

If a scatter diagram is football shaped, it can be summarized using the 5-number summary:

Variable Description
ave_x
SD_x
ave_y
SD_y
r

Association

  • Positive association is demonstrated when the dots are trend upward as x increases (r is positive).
  • Negative association is demonstrated when the the dots trend downward as x increases (r is negative).
  • Strong association is demonstrated when dots are clustered tightly together along a line (|r| is closer to 1).
  • Weak association is demonstrated when dots are not clustered tightly. (|r| is closer to 0)

Correlation

Correlation is between -1 and 1. Correlation near 1 means tight clustering, and correlation near 0 means loose clustering. r is -1 if the points are on a line with negative slope, r is positive 1 if the points are on a line with a positive slope. As |r| gets closer to 1, the line points cluster more tightly around a line.

Terminology

Term Definition
r Correlation Coefficient
Linear Correlation Measures the strength of a line