Chapter 11--Regression and Correlation Methods

Chapter 11 regression and correlation methods stat

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Unformatted text preview: = 0 is to reject H0 if F= MSR ≥ F1−α,1,n−2 . MSE This test is rather more intuitive that the t -test we discussed before, but the advantage of the t -test is that it can also be use for one-sided hypothesis as well. 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 ANOVA for Simple Linear Regression Cont’d.. In R, ANOVA table can be produced by the anova() command. For the birthweight-estriol example, Analysis of Variance Table Response: bw Df Sum Sq Mean Sq F value Pr(>F) estriol 1 250.57 250.574 17.162 0.0002712 *** Residuals 29 423.43 14.601 --Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 Estriol level has a significant predictive value for the variation in birthweight. Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics 1 Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Coefficient of Determination (R 2 ) Coefficient of Determination (R 2 ): is the proportion (fraction) of the total variation in the observed responses (y) that can be explained by (accounted for by) the simple linear regression on x. SSR . R2 = TSS Obviously, 0 ≤ R 2 ≤ 1. For the birthweight-estriol example, R 2 = 250.57/(250.57 + 423.43) = 37%. Therefore, 37% of the variation observed in the birthweight can be explained by the estriol level. 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 Predicting the Expected Response We are interested in predicting the mean (expected) birthweight of all women with a given estriol level. That is, we are interested in estimating µyn+1 |xn+1 for the new value of the independent variable denoted by...
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