L09-09 - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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10/01/09 Lecture 9 1 STOR 155 Introductory Statistics Lecture 9: Cautions about Regression and Correlation, Causation The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
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10/01/09 Lecture 9 2 Review • Least-Squares Regression Lines • Equation and interpretation of the line • Prediction using the line • Correlation and Regression • Coefficient of Determination
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10/01/09 Lecture 9 3 Regression Diagnostics • Look at residuals (errors): – A residual is the difference between an observed value of the response variable and the value predicted by the regression line, i.e., – The sum of the least-squares residuals is always zero. . ˆ residual y y Why?
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10/01/09 Lecture 9 4 Residual Plots • A residual plot is a scatterplot of the regression residuals against the explanatory variable. • Residual plots help us assess the fit of a regression line.
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10/01/09 Lecture 9 5 Age vs Height
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10/01/09 Lecture 9 6 Residual Plot • If the regression line catches the overall pattern of the data, there should be no pattern in the residual. totally random
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10/01/09 Lecture 9 7 nonlinear nonconstant variation
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10/01/09 Lecture 9 8 Diabetes Patient: FPG vs HbA • FPG: fasting plasma glucose. • HbA: percent of red blood cells that have a glucose molecule attached. • Both are measuring blood glucose. • We expect a positive association. • 18 subjects, r = 0.4819. • See the scatterplot on the next page.
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10/01/09 Lecture 9 9 Diabetes Patient: FPG vs HbA
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10/01/09 Lecture 9 10 Outliers and Influential Observations • An outlier is a point that lies outside the overall pattern of the other points. – Outliers in the y direction have large residuals, but
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L09-09 - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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