# 16 Correlation - Two variables Which test Explanatory...

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Unformatted text preview: Two variables: Which test? Explanatory variable Categorical Numerical Categorical Contingency analysis Logistic regression Survival analysis Response variable Numerical t-test Analysis of variance Regression Correlation Correlation: r • ! Describes the relationship between two numerical variables • ! Parameter: ! (rho) Estimate: r Max. lifespan of females (days) 12.5 15.0 17.5 20.0 22.5 25.0-1 1 2 3 4 Number of males per female C. elegans data r 2 = 0.93 %adults who smoke 15 20 25 30 10 20 30 40 50 60 70 80 90 Excise tax (c/pack) Smoking/taxes data r 2 = 0.12 r = - 0.98 r = - 0.35 Correlation assumes... • ! Random sample • ! X is normally distributed with equal variance for all values of Y • ! Y is normally distributed with equal variance for all values of X Correlation coefficient facts • !-1 < ! < 1 • ! Coefficient of determination: r 2 : Describes the proportion of variation in one variable that can be predicted from the other Estimating the correlation coefficient r =...
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16 Correlation - Two variables Which test Explanatory...

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