BPS4e_chapter04

# BPS4e_chapter04 - Relationships Scatterplots and...

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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
Student Number of Beers Blood Alcohol Level 1 5 0.1 2 2 0.03 3 9 0.19 6 7 0.095 7 3 0.07 9 3 0.02 11 4 0.07 13 5 0.085 4 8 0.12 5 3 0.04 8 5 0.06 10 5 0.05 12 6 0.1 14 7 0.09 15 1 0.01 16 4 0.05 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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Student Beers BAC 1 5 0.1 2 2 0.03 3 9 0.19 6 7 0.095 7 3 0.07 9 3 0.02 11 4 0.07 13 5 0.085 4 8 0.12 5 3 0.04 8 5 0.06 10 5 0.05 12 6 0.1 14 7 0.09 15 1 0.01 16 4 0.05 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 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?
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 … Form: linear, curved, clusters, no pattern Direction: positive, negative, no direction Strength: how closely the points fit the “form” … and deviations from that pattern. Outliers

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## This note was uploaded on 06/24/2008 for the course MATH 1070 taught by Professor Akbas during the Summer '08 term at Georgia State.

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BPS4e_chapter04 - Relationships Scatterplots and...

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