# chapter2 - Chapter 2 Looking at Data Relationships...

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Chapter 2 Looking at Data - Relationships

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Relations Among Variables Response variable - Outcome measurement (or characteristic) of a study. Also called: dependent variable, outcome , and endpoint . Labelled as y . Explanatory variable - Condition that explains or causes changes in response variables. Also called: independent variable and predictor. Labelled as x . Theories usually are generated about relationships among variables and statistical methods can be used to test them. Research questions are stated such as: Do changes in x cause changes in y ?
Scatterplots Identify the explanatory and response variables of interest, and label them as x and y Obtain a set of individuals and observe the pairs ( x i , y i ) for each pair. There will be n pairs. Statistical convention has the response variable ( y ) placed on the vertical (up/down) axis and the explanatory variable ( x ) placed on the horizontal (left/right) axis. (Note: economists reverse axes in price/quantity demand plots) Plot the n pairs of points ( x , y ) on the graph

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France August,2003 Heat Wave Deaths Individuals: 13 cities in France Response: Excess Deaths(%) Aug1/19,2003 vs 1999-2002 Explanatory Variable: Change in Mean Temp in period (C) Data: City Dth03 Dth9902 %chng (y) Degchg(x) Little 200 192.3 4 4 Marseilles 571 456.8 25 4.3 Grenoble 148 115.6 28 6.3 Rennes 156 114.7 36 5.6 Toulouse 315 231.6 36 6.6 Bordeaux 318 222.4 43 6.2 Strasbourg 253 167.5 51 5.9 Nice 341 222.9 53 4.3 Poitiers 184 102.8 79 7.3 Lyon 447 248.3 80 6.8 Le Mans 204 112.1 82 7 Dijon 168 87 93 7.4 Paris 1854 766.1 142 6.7
France August,2003 Heat Wave Deaths 2003 France Heat Wave Mortality 0 20 40 60 80 100 120 140 160 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 Change in Mean Temp (Celsius) Excess Mortality (%) Possible Outlier

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Example - Pharmacodynamics of LSD Score (y) LSD Conc (x) 78.93 1.17 58.20 2.97 67.47 3.26 37.47 4.69 45.65 5.83 32.92 6.00 29.97 6.41 Response ( y ) - Math score (mean among 5 volunteers) Explanatory ( x ) - LSD tissue concentration (mean of 5
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chapter2 - Chapter 2 Looking at Data Relationships...

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