30 Mar 2012

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Chapter 14

Describing Relationships: Scatterplots and Correlation

Principles that guide our work:

1) First plot the data, then add numerical summaries

2) Look for overall patterns and deviations from those patterns

3) When the overall pattern is quite regular, there is sometimes a way to describe it very briefly

Scatterplots

The most common way to display the relation between two quantitative variables is a scatterplot

A scatterplot shows the relationship between two quantitative variables measured on the same

individuals

o The values of one variable appear on the horizontal axis, and the values of the other

variable appear on the vertical axis

o Each individual in the data appears as the point in the plot fixed by the values of both

variables for that individual

Always plot the explanatory variable if there is one, on the horizontal axis of a scatterplot

If there is no explanatory response distinction, either variable can go on the horizontal axis

The response variable y

Interpreting scatterplots

Look for the overall pattern and for striking deviations from that pattern

You can describe the overall pattern of a scatterplot by the direction, form, and strength of the

relationship

An important kind of deviation is an outlier, an individual value that falls outside the overall

pattern of the relationship

Two variables are positively associated when above-average values of one tend to accompany

above-average values of the other and below-average values also tend to occur together

The scatterplot slopes upward as we move from left to right

Two variables are negatively associated when above-average values of one tend to accompany

below-average values of the other, and vice versa

The scatterplot slopes downward from left to right

The strength of a relationship in a scatterplot is determined by how closely the points follow a

clear form

Correlation

Straight-line relations are important because a straight line is a simple pattern that is quite

common

Correlation describes the direction and strength of a straight-line relationship between two

quantitative variables written as r

positive r indicates positive association between the variables, and negative r indicates negative

association

the correlation r always falls between -1 and 1