Section 7.1 ~ Seeking Correlation Introduction to Probability and Statistics Ms. Young ~ room 113

Sec. 7.1 Objective After this section you will be able to define correlation, recognize positive and negative correlations on scatter diagrams, and understand the correlation coefficient as a measure of the strength of a correlation.

Sec. 7.1 Scatter Diagrams A scatter diagram (or scatterplot) is a graph that represents the values of two variables using dots

Sec. 7.1 Correlation A correlation is a relationship between two variables and can be seen easily using a scatterplot A positive correlation occurs when both variables increase (or decrease) together Ex. ~ Number of shoes sold and money made; the more shoes that are sold will result in more money being made A negative correlation occurs when one variable increases while the other decreases Ex. ~ Number of people and group rate; as the number of people increases, the group rate goes down Ex. ~ Age and life expectancy; as you get older, your life expectancy gets lower No correlation occurs when there is no apparent (linear) relationship between the two variables Ex. ~ Temperature and shoe size; as your temperature increases (or decreases), your shoe size does not increase (or decrease) A nonlinear relationship is when there is a relationship between the two variables, but not a linear one Ex. ~ Time passed and height of a softball after being thrown straight up in the air; as the time increases, the height of the ball will increase, but then reach a maximum height and begin to decrease. This represents a quadratic relationship and would therefore be nonlinear

Positive Correlations Sec. 7.1 Positive Correlations Types of positive correlations: Perfect Positive Correlation – when both values increase and fall in a straight line (y is directly related to x) High (or strong) Positive Correlation – when both values increase and are tightly clustered around a straight line Low (or weak) Positive Correlation – when both values increase and are somewhat clustered around a straight line

Negative Correlations Sec. 7.1 Negative Correlations Types of negative correlations: Perfect Negative Correlation – when one value increases and the other decreases and they fall in a straight line High (or strong) Negative Correlation – when one value increases and the other decreases and they are tightly clustered around a straight line Low (or weak) Negative Correlation – when one value increases and the other decreases and they are somewhat clustered around a straight line

No Correlation & Nonlinear Correlations Sec. 7.1 No Correlation & Nonlinear Correlations Scatterplots representing no correlation Scatterplot representing a nonlinear correlation

Correlation Coefficient Sec. 7.1 Correlation Coefficient A correlation coefficient (r) is a numerical value that represents the strength and direction of a correlation The correlation coefficient can only range from 1 to -1, where 1 is a perfect positive correlation and -1 is a perfect negative correlation No correlation would have a correlation coefficient close to 0 A positive correlation will only range from 0 to 1 where stronger correlations are closer to 1 and weaker correlations are closer to 0 A negative correlation will only range from 0 to -1 where stronger correlations are closer to -1 and weaker correlations are closer to 0 To calculate the correlation coefficient by hand, use the following formula: But don’t worry, we won’t be calculating it by hand!