Chapter_3_2 - Quick Review of Last Lecture Chapter 3:...

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Chapter 3: Association: Contingency, Correlation, and Regression (cont) Read Chapter 3 Quick Review of Last Lecture ± World is complex and multivariate ± We will introduce some tools to visualize relationships between pairs of variables ± Response variable (Dependent Variable) the outcome variable on which comparisons are made ± Explanatory variable (Independent variable) defines the groups to be compared with respect to Association ± The main purpose of data analysis with two variables is to investigate whether there is an association and to describe that association ± An association exists between two variables if a particular value for one variable is more likely to occur with certain values of the other variable Linear Correlation, r ± Measures the strength and direction of the linear association between x and y ² A positive r value indicates a positive association ² A negative r value indicates a negative association ² An r value close to +1 or -1 indicates a strong linear association ² An r value close to 0 indicates a weak association ) )( ( 1 1 y x s y y s x x n r = Properties of Correlation ± Always falls between -1 and +1 ± Sign of correlation denotes direction ² (-) indicates negative linear association ² (+) indicates positive linear association ± Correlation has a unitless measure - does not depend on the variables’ units ± Two variables have the same correlation no matter which is treated as the response variable ± Correlation is not resistant to outliers ± Correlation only measures strength of linear relationship Some Association Plots ± Quantitative vs Quantitative ² Scatterplots ± Quantitative vs Qualitative Variables ² Boxplots ± Quant-Quant-Qual ² Coded Scatterplots
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Canadian Prestige Data 1. Education - Average education of occupational incumbents, years, in 1971. 2. Income - Average income of incumbents, dollars, in 1971. 3. Women - Percentage of incumbents who are women. 4. Prestige - Pineo-Porter prestige score for occupation, from a social survey conducted in the mid-1960s. 5. Census -Canadian Census occupational code. 6. Type - type of occupation. A factor with levels ± bc, Blue Collar; ± prof, Professional, Managerial, and Technical; ± wc, White Collar. Quantitative vs Quantitative: Scatterplots ² Trend (pattern) – linear or curvilinear ² Direction – increasing/decreasing (positive/negative) ² Strength of association – look at the amount/width of scatter ² Outliers – data points that don’t follow the pattern 6 8 10 12 14 16 20 40 60 80 education prestige 5000 10000 15000 20000 25000 income 02 04 06 08 01 0 0 women Describing the relationship between variables 6 8 10 12 14 16
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Chapter_3_2 - Quick Review of Last Lecture Chapter 3:...

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