LectureOct29

# LectureOct29 - Linear Regression II. Estimating Trends from...

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1 Linear Regression II. Estimating Trends from a Sample C. Standard Error of Regression Coefficients III. Hypothesis Testing A. Significance of Trend B. CI for Line of Means C. CI for Observations IV. Comparing Regression Lines A. Hypothesis Test of Slope B. Overall Test of Coincidence V. Correlation A. Correlation Coefficient Glantz p 278-296 Estimating Trends from a Sample

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2 • Regression line of y on x ˆ y ab x = + Least-squares Regression 22 () ii i i nx y x y b x = ∑∑ 2 i yx xx y a x = ay b x = −⋅ Line of means x μ αβ = + The line of means ˆ y x = + Regression line Least-squares Regression Estimate of the line of means σ 2 1 2 y x n ss b s n =−
3 2 2 1 (1 ) ay x x x ss nn s =+ 1 1 y x b x s s s n = s a = (.096 g ) 1 10 (36.9 cm ) 2 (10 1)(5.0 cm ) 2 = 2.4 g s b = 1 10 1 .096 g 5.0 cm = 0.06 g / cm Standard Error of Regression Coefficients Standard error for the estimate a Standard error for the estimate b In the example t statistic: b parameter estimate true value of poplulation parameter b t standard error of parameter estimate s β == t = b s b Is there a relationship between variables??? v = n 2 III. Hypothesis Testing: A. Significance of Trend 0: 0 H =

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4 b = 0.50 g / cm s b = 0.06 g / cm t = b s b = 8.33 v = n 2 = 8 t 0.001 = 5.401 H0 = There is no relationship between height and weight in Martians t > t 0.001 Conclusion: Reject H0 (P<0.001) In the Example
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## This note was uploaded on 12/02/2008 for the course BME 423 taught by Professor D'argenio during the Fall '06 term at USC.

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LectureOct29 - Linear Regression II. Estimating Trends from...

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