Chapter 11--Regression and Correlation Methods

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Unformatted text preview: 0 q q q q q q q q q q x 1 q q q q rxy = 0 0 q q 5 −1 q q q q q −2 q q q q q q q q 2 q q q q q q q q q q −10 6 q q q q q q q q q q q q q q q q q −5 y 8 q q q 0 12 10 q q q q q q q q q q q q q q q 5 10 15 x Stat 491: Biostatistics 20 25 Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Example In R, correlation can be computed by the cor() command. For the birthweight-estriol example, rxy = 0.6097. There is a moderate correlation. In R, this is computed using cor(x=estriol,y=bw, method="pearson") 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 Inference about the Population Correlation Coeﬃcient ρxy Assumptions: (xi , yi ) are independently and identically distributed as normal for i = 1, . . . , n. That is, there is no notion of dependent and independent variable. Correlation coeﬃcients can be aﬀected by systematic choice of x values. This may result in a biased estimate of the population correlation coeﬃcient ρxy . Example: age speciﬁc recruitment of patients and use rxy to estimating the population correlation between outcome and age. 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 A Statistical Test for ρxy The hypotheses H0 : ρxy = 0 vs Ha : ρxy = 0. Test statistic √ n−2 t = rxy . 2 1 − rxy Reject H0 if |t | ≥ t1−α/2,n−2 . The R command cor.test can do this test. One sided test can be constructed in the usual way. ˆ There is an interesting relationship between β1 and rxy given by ˆ β1 = rxy Syy . Sxx The t test for correlation and slope give the same answer. 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 Test for H0 : ρxy = ρ0 when ρ0 = 0 Deﬁn...
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## This note was uploaded on 02/03/2014 for the course STAT 491 taught by Professor Solomonharrar during the Fall '12 term at Montana.

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