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Unformatted text preview: Scatterplots Measuring Association Spurious Correlation Outline Scatterplots Measuring Association Covariance Correlation Spurious Correlation 1 / 13 ISOM 2500 Lect 4: Association btw Numerical Variables Scatterplots Measuring Association Spurious Correlation Example, Natural Gas Consumption vs Climate • Is household natural gas consumption associated with climate? • Annual household natural gas consumption measured in thousands of cubic feet (MCF) • Climate as measured by the National Weather Service using heating degree days (HDD) • Response : the variable whose variation is of interest • Natural gas consumption in this example • Explanatory variable : the variable that’s used to explain the variation in the response • Heating degree days in this example • Scatterplot : A graph displaying pairs of values as points on a twodimensional plane • The explanatory variable is placed on the xaxis • The response is placed on the yaxis 2 / 13 ISOM 2500 Lect 4: Association btw Numerical Variables Scatterplots Measuring Association Spurious Correlation Scatterplot Scatterplot of Natural Gas Consumption (y) versus Heating DegreeDays (x) 1 1 This output is obtained using Analyze > Fit Y by X with Natural Gas as Y and Heating DD as X. 3 / 13 ISOM 2500 Lect 4: Association btw Numerical Variables Scatterplots Measuring Association Spurious Correlation Describing Association • Direction. Does the pattern trend up, down, or both? • Curvature. Is the pattern linear or curved? • Variation. Are the points tightly clustered around the trend? • Outliers. Is there something unexpected? Gas Consumption vs. Heating Degree Days: • Direction: Trend up . • Curvature: Linear . • Variation: Considerable scatter . • Outliers: None apparent . 4 / 13 ISOM 2500 Lect 4: Association btw Numerical Variables Scatterplots Measuring Association Spurious Correlation Covariance Correlation Covariance Cov ( x , y ) = ( x 1 ¯ x )( y 1 ¯ y ) + ( x 2 ¯ x )( y 2 ¯ y ) + ··· + ( x n ¯ x )( y n ¯ y ) n 1 : a measure that quantifies the linear association...
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