Chapter 11--Regression and Correlation Methods

# 2 box plot and q q plot of residuals are used to

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Unformatted text preview: ed in R to extract the studentized residuals and ﬁtted values. If all the points are contained in a horizontal band without any outlier or trend, that means no indication of the violation linearity and constant variance. If the points cover a cone shaped region, that is an indication of the violation of constant variance assumption. 2 Box plot and Q-Q plot of Residuals: are used to check normality. How do we check the assumption of independence? (Hard) 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 Residual Plots: Three Examples Normal Q−Q Plot Normal Q−Q Plot −2 −1 0 1 2 20 q 10 Sample Quantiles 5 qq q q q −15 q q qqq q q qqq qq q q −2 −1 0 1 2 q qqq qq qq q q q −2 −1 0 1 q q 20 0 10 5 1 −20 q q q q q q q q q q q q q q q x q q q 10 q ^ y − µy 5 x 0 ^ y − µy q q −5 q 20 q q q q q q q q q q q q 8 ^ µy q q 10 12 q q q q q q 4 5 x Chapter 11: Regression and Correlation Methods 6 7 ^ µy 8 9 q q q q −20 q 6 q q q q q q −15 1 x 0 ^ y − µy q q q q −1 q q q q −2 q q 4 q q q q 10 q q q q q 30 q q q 0 −2 −15 −1 0 −5 0 2 Theoretical Quantiles 30 Theoretical Quantiles 10 Theoretical Quantiles q q qqq q q q q −20 −1 q q q qqq qqq q 30 10 qqq q q q 0 q qq q q q −5 qqq q Sample Quantiles 1 0 q −2 Sample Quantiles q q q q q qq q 0 Normal Q−Q Plot q 0 20 40 60 ^ µy x Stat 491: Biostatistics x 80 100 120 Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Residual Analysis: BirthWeight-Estriol Studentaized 6 2 Studentaized 2 Plot of Stu. Resid. vs Predi. q q q q q 1 q q q q q q q q q q q qqq q 0 0 q Sample Quantiles q q −1 0 q −2 res 2 q q qq q qq q qq q q qq qq q q q q q q −1 1 4 q q qqq q qq qqq −6 −2 −2 −4 q q q 25 30 35 40 −2 fit Chapter 11: Regression and Correlation Methods −1 0 1 Theoretical Quantiles Stat 491: Biostatistics 2 Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequac...
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