501_Lecture_02 - Sections 2.1-2.2 Looking at...

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Sections 2.1-2.2 Looking at Data-Relationships
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Data with two or more variables: Response vs Explanatory variables Scatterplots Correlation Regression line
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Association between a pair of variables Association: Some values of one variable tend to occur more often with certain values of the other variable Both variables measured on same set of individuals Examples: Height and weight of same individual Smoking habits and life expectancy Age and bone-density of individuals
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Causation? Caution: Often there are spurious, other variables lurking in the background Shorter women have lower risk of heart attack Countries with more TV sets have better life expectancy rates More deaths occur when ice cream sales peak Just explore association or investigate a causal relationship?
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Preliminaries: Who are the individuals observed? What variables are present? Quantitative or categorical ? Association measures depend on types of variables Response variable measures outcome of interest Explanatory variable explains and sometimes causes changes in response variable
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Examples Different amount of alcohol given to mice, body temperature noted (belief: drop in body temperature with increasing amount of alcohol) Response variable? Explanatory variable? SAT scores used to predict college GPA Response variable? Explanatory variable?
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Examples Does fidgeting keep you slim? Some people don’t gain weight even when they overeat. Perhaps fidgeting and other “nonexercise activity” explains why, here is the data: We want to plot Y vs. X Which is Y? Which is X?
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Things to look for on scatterplot: Form (linear, curve, exponential, parabola) Direction: Positive Association : Y increases as X increases Negative Association : Y decreases as X increases Strength: Do the points follow the form quite closely or scattered? Outliers: deviations from overall relationship Let’s look again…
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Example: State mean SAT math score plotted against the percent of seniors taking the exam
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Adding a categorical variable or grouping May enhance understanding of the data Categorical variable is (region): e is for northeastern states m is for midwestern states All others states excluded
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Example: Adding categorical variable
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Other things: Plotting different categories via different symbols may throw light on data Read examples 2.7-2.9 for more examples of scatterplots Existence of a relationship does not imply causation
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