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Chapter04

# The Basic Practice of Statistics (Paper) & Student CD

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Relationships Scatterplots and correlation BPS chapter 4 © 2006 W.H. Freeman and Company

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Objectives (BPS chapter 4) Relationships: Scatterplots and correlation Explanatory and response variables Displaying relationships: scatterplots Interpreting scatterplots Adding categorical variables to scatterplots Measuring linear association: correlation Facts about correlation
0.05 4 16 0.01 1 15 0.09 7 14 0.1 6 12 0.05 5 10 0.06 5 8 0.04 3 5 0.12 8 4 0.085 5 13 0.07 4 11 0.02 3 9 0.07 3 7 0.095 7 6 0.19 9 3 0.03 2 2 0.1 5 1 Blood Alcohol Level Number of Beers Student Here we have two quantitative variables for each of 16 students. 1. How many beers they drank, and 2. Their blood alcohol level (BAC) We are interested in the relationship between the two variables: How is one affected by changes in the other one?

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0.05 4 16 0.01 1 15 0.09 7 14 0.1 6 12 0.05 5 10 0.06 5 8 0.04 3 5 0.12 8 4 0.085 5 13 0.07 4 11 0.02 3 9 0.07 3 7 0.095 7 6 0.19 9 3 0.03 2 2 0.1 5 1 BAC Beers Student Scatterplots In a scatterplot one axis is used to represent each of the variables, and the data are plotted as points on the graph.
Explanatory (independent) variable: number of beers Blood Alcohol as a function of Number of Beers 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0 1 2 3 4 5 6 7 8 9 10 Number of Beers Blood Alcohol Level (mg/ml) Response (dependent) variable: blood alcohol content x y Explanatory and response variables A response variable measures or records an outcome of a study. An explanatory variable explains changes in the response variable. Typically, the explanatory or independent variable is plotted on the x axis and the response or dependent variable is plotted on the y axis.

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Some plots don’t have clear explanatory and response variables . Do calories explain sodium amounts? Does percent return on Treasury bills explain percent return on common stocks?
Apply your knowledge Go to pages 92-94 and work on the following problems: 4.1 Explanatory and response variables? 4.2 Coral reefs 4.3 Beer and blood alcohol 4.4 Bird colonies

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Interpreting scatterplots After plotting two variables on a scatterplot, we describe the relationship by examining the form , direction , and strength of the association. We look for an overall pattern …
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Chapter04 - Relationships Scatterplots and correlation BPS...

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