Scatterplots, Association, and Correlation PDF

Chapter 6 : Scatterplots, association and correlation p177 Previously, single variables on their own. Or one or more categorical variables. Now look at two quantitative variables. First tool: scatterplot. – Plot values of two quantitative variables against e...

Chapter 6 : Scatterplots, association and correlation p177 Previously, single variables on their own. Or one or more categorical variables. Now look at two quantitative variables. First tool: scatterplot. – Plot values of two quantitative variables against each other (scatterplot). 1  Scatterplots, association and correlation p181 When examining the relationship between two or more variables, first think about whether some variables are response (dependent) variables and others explanatory (independent) variables? Sometimes called x and y-variables. 2  Scatterplots, association and correlation p179 Example Row Wine Heart disease 1 2.5 211 2 3.9 167 3 2.9 131 18 1.2 199 19 2.7 172 Explanatory variable? Response variable? 3 Scatterplots, association and correlation How do we describe this information? 4  Describing scatterplots p179 Look for – overall pattern – and striking deviations from that pattern. The overall pattern of a scatterplot can be described by the – form – direction – and strength of the relationship. – An important kind of deviation is an outlier, an individual value that falls outside the overall pattern. 5  Describing scatterplots p179 The overall pattern of a scatterplot can be described by the – Form Linear Non-linear – direction Positive ( One increases as the other one increases) Negative (One decreases as the other one increases) – and strength of the relationship. Strong Moderate Weak 6 Interpretation (wine data) Form: Linear Direction: Negative This means that higher levels of wine consumption are associated with lower death rates. Strength: Moderate No outliers 7  Interpretation (wine data) The direction of the association between wine intake and heart diseases is negative. Does this mean that one should drink a lot of wine if s/he is concerned about heart diseases? This does not mean there is a causal effect. There could be a lurking variable. Higher wine consumption could be linked to higher income, which would allow better medical care. 8  R commands for scatterplots wt