Chapter 11--Regression and Correlation Methods

1 we reject h0 if t t12n2 for ones sided test we use

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: has no predictive value for change in y is formulated as H0 : β1 = 0 vs Ha : β1 = 0. Test statistic t= ˆ β1 . σβ1 ˆˆ We reject H0 if |t | ≥ t1−α/2,n−2 . For ones sided test we use t1−α,n−2 . ˆ 100(1 − α)% confidence interval for β1 is β1 ± t1−α/2,n−2 σβ1 . ˆˆ Similar procedures can be developed for β0 . 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 Cont’d... Statistical significance in the birthweight-estriol example. In R, the summary() command produces the desired output. Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 21.5234 2.6204 8.214 4.68e-09 *** estriol 0.6082 0.1468 4.143 0.000271 *** Confidence intervals can be generated by using the confint() command 2.5 % 97.5 % (Intercept) 16.1640740 26.8827831 estriol 0.3079268 0.9084542 The intervals are rather wide which is not surprising due to the small sample size. 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 Analysis of variance (ANOVA) It can be shown that (y − y )2 = ¯ (µy |x − y )2 + ˆ ¯ (y − µy |x )2 . ˆ Tot. Obs. Variation = Var. due to Regr. + Unexplained Var. A concise notation is, TSS = SSR + SSE . The total degrees of freedom n − 1 also partitions into the regression degrees of freedom 1 and the error degrees of freedom n − 2. That is, dfTot = dfReg + dfError . 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 Cont’d ... Mean Squares are defined in the usual way by dividing SS with the corresponding df . That is, MSR = SSR 1 and MSE = SSE . n−2 An alternative α level F -test for the hypothesis H0 : β1 = 0 vs Ha : β1...
View Full Document

Ask a homework question - tutors are online