galton - Bivariate Normal Distribution and Regression...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

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

Unformatted text preview: Bivariate Normal Distribution and Regression Application to Galton’s Heights of Adult Children and Parents Sources: Galton, Francis (1889). Natural Inheritance, MacMillan, London. Galton, F.; J.D. Hamilton Dickson (1886). “Family Likeness in Stature”, Proceedings of the Royal Society of London , Vol. 40, pp.42-73. Data – Heights of Adult Children and Parents • Adult Children Heights are reported by inch, in a manner so that the median of the grouped values is used for each (62.2”,…,73.2” are reported by Galton). – He adjusts female heights by a multiple of 1.08 – We use 61.2” for his “Below” – We use 74.2” for his “Above” • Mid-Parents Heights are the average of the two parents’ heights (after female adjusted). Grouped values at median (64.5”,…,72.5” by Galton) – We use 63.5” for “Below” – We use 73.5” for “Above” Adult Child vs Mid-Parent Height 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 63 64 65 66 67 68 69 70 71 72 73 Mid-Parent Adult Child Mid-Parent Height 50 100 150 200 250 63.5 64.5 65.5 66.5 67.5 68.5 69.5 70.5 71.5 72.5 Height Frequency Adult Child Heights 20 40 60 80 100 120 140 160 180 61.2 62.2 63.2 64.2 65.2 66.2 67.2 68.2 69.2 70.2 71.2 72.2 73.2 74.2 Height Frequency Joint Density Function ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 [ ] 2 1 2 2 1 1 2 2 2 2 2 1 2 1 1 1 2 1 2 2 2 2 2 2 1 2 2 1 1 2 1 2 1 1 2 2 2 2 2 1 2 1 ) ( ) ( ) ( ) ( : where , 2 1 2 1 exp 1 2 1 ) , ( σ σ μ μ ρ σ μ σ μ σ μ σ σ μ μ ρ σ μ ρ ρ σ σ π-- = = = = = ∞ < < ∞- - +---- --- = Y Y E Y V Y E Y V Y E y y y y y y y y f 0.05 0.1 0.15 0.2-3-2.5-2-1.5-1-0.5 0.5 1 1.5 2 2.5 3 x1 Bivariate Normal Density 0.15-0.2 0.1-0.15 0.05-0.1 0-0.05 μ 1 = μ 2 = 0 σ 1 = σ 2 = 1 ρ= 0 .4 Marginal Distribution of Y 1 (P. 1) ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 [ ] ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 [ ] ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 [ ] ( 29 ( 29 [ ] 2 2 2 2 2 1 1 2 1 2 2 2 2 1 2 2 1 1 2 2 2 2 1 1 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 1 1 2 2 2 2 1 1 2 1 2 2 2 2 1 2 2 1 1 2 2 2 1 1 2 2 2 1 2 2 2 2 2 1 2 2 2 2 1 1 2 2 1 2 2 2 2 1 2 2 1 1 2 2 2 1 1 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 2 2 1 2 2 1 1 2 1 2...
View Full Document

This note was uploaded on 06/04/2011 for the course STA 4321 taught by Professor Staff during the Spring '08 term at University of Florida.

Page1 / 17

galton - Bivariate Normal Distribution and Regression...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online