Chapter 11--Regression and Correlation Methods

A high inuence point is a point with x outlier and y

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Unformatted text preview: y of Fit Correlation Multiple Regression High Leverage and High Influence Points High leverage point is a point that has very high or very low value of the independent variable (outlier in the x -direction). A high influence point is a point with x -outlier and y -outlier. High influence point is a point whose omission will change the regression substantially. A high leverage point indicates only a potential distortion of the regression equation. Statistical Softwares typically calculate diagnostic measures of leverage and influence. Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression 35 30 30 35 High Leverage and High Influence Points Cont’d ... Outlier Outlier 25 q 25 q y y Including Outlier 20 Including Outlier 15 q 20 q q q q 15 q q q 10 Excluding outlier 10 Excluding outlier 0 5 10 15 x Chapter 11: Regression and Correlation Methods 0 5 10 x Stat 491: Biostatistics 15 Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression What is correlation? Correlation: is a measure of the strength of linear relationship between x and y . The stronger the correlation, the better x predicts y . Correlation between x and y is denoted by rxy and is given by rxy = Sxy Sxx Syy where Syy = (y − y )2 = TSS . ¯ Always, −1 ≤ rxy ≤ 1 Low correlation only means no linear relationship. R 2 the square of the correlation coefficient rxy . Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Interpretation of rxy rxy = − 0.898 14 rxy = 0.946 q 4 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q y q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 10 15 20 25 5 10 15 0 2 q q q q y q q q q q q q q q q q q q q q q q q q q q q q q q q −50 q q q q q q q q q q q q q q q q q q q q q q q 15 q q q q q q q q q q q q q q q q q q q q q q q q q q q q 25 x Chapter 11: Regression and Correlation Methods q q q −150 20 q q q q q 10 q q q q q q q q 5 q q q q q q q q q q q q y q q q q q q q −100 q q q q q q q q q q 25 x q q 20 rxy =...
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