Transcript Section 7.1 ~ Seeking Correlation

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


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. ~ Number of shoes sold and money made; the more shoes that are sold
will result in more money being made
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
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

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

Sec. 7.1
No Correlation & Nonlinear Correlations

Scatterplots representing no correlation

Scatterplot representing a nonlinear correlation
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:
r

n  ( x  y )  (x)  (y )
n  (x 2 )  (x) 2  n  (y 2 )  (y ) 2
But don’t worry, we won’t be calculating it by hand!