东南大学：《统计学》课程教学资源（PPT课件）第十章 回归与相关 CORRELATION & REGRESSION

Lecture 10 correlation REGRESSION Xiaojin Yu Department of Epidemiology and Biostatistics, public Health school Southeast university

1 Lecture10 CORRELATION & REGRESSION Xiaojin Yu Department of Epidemiology and Biostatistics, public Health school, Southeast University

revew a Comparison of means t-test a Comparison of proportions Chi-square test Comparison of Median Rank sum test

2 review ◼ Comparison of means :t –test ◼ Comparison of proportions: Chi-square test ◼ Comparison of Median: Rank sum test

Review on rank sum test - raw data and Rank cardinal and ordinal number) Rank sum test methods based on rank a 2 independent groups willcoxon rank sum test 2 paired groups sign rank sum test

Review on rank sum test ◼raw data and Rank ( cardinal and ordinal number) ◼Rank sum test_ methods based on rank ◼2 independent groups_ willcoxon rank sum test ◼2 paired groups_ sign rank sum test 3

Solution to height comt p arison height between F and M 65 TM=52 T26 (N+1)12×13 78 2 N+1 6.5 ■B| ue-male ■Red-fema|e

Solution to height comparison height between F and M ◼ Blue-male ◼ Red- female 4 12 11 10 8 6 5 TM=52 9 7 4 3 2 1 Tf=26 6.5 2 1 78 2 12 13 2 ( 1) = + =  = + N N N

eXAMPLE 9.1 Table 9.1 Survival Times of Cats rabbits without oxygen Cats r abb its minutes ra ink minutes rank 25 9.5 14 34 13 15 44 15 16 46 16 12345 17 19 18 6.5 19 6.5 20 23 25 89 5 28 30 12 35 n1=8 =127.5m2=12 T=82.5

5 EXAMPLE 9.1: Table 9.1 Survival Times of Cats & Rabbits without oxygen T2 n =82.5 2 T =12 1 n =127.5 1 =8 35 14 30 12 28 11 25 9.5 50 20 23 8 49 19 21 6.5 48 18 21 6.5 46 17 19 5 46 16 17 4 44 15 16 3 34 13 15 2 25 9.5 14 1 minutes rank minutes rank Cats rabbits

Solution to Example9. 1 population critical interval of T locations of survival time of 065(58 both cat and ra bbit are equal 110),T=127.5, is beyond of T H,: Mi# M2 population locations S0,P<u, Given o=0.05,P<0.05 of survival time of both cat and Ho is rejected, it concludes that the rabbit are not equal survival times of cats and a=0.05 rabbits in the environment Sorting and ranking calculate 2 Rank sums of 2 groups. Take without oxygen might be the li wIth small as T different n1=8<n2=12,s0T=T1=127.5

Solution to Example9.1 ◼ H0 ： M1=M2 population locations of survival time of both cat and rabbit are equal H1： M1 ≠ M2 population locations of survival time of both cat and rabbit are not equal ； a = 0.05 ◼ Sorting and ranking, calculate 2 Rank sums of 2 groups. Take the Ti with small n as T. n1=8<n2=12, so T= T1 =127.5. ◼ critical interval of T0.05 (58- 110),T=127.5, is beyond of Tα , so, P≤α, Given α=0.05, P<0.05; H0 is rejected, it concludes that the survival times of cats and rabbits in the environment without oxygen might be different. 6

Basic logics of scientific research ■ To find the difference To find the correlation

Basic logics of scientific research ◼ To find the difference ◼ To find the correlation

Contents ■| inear Correlation ■ Rank correlation simple linear regression

Contents ◼ linear Correlation ◼Rank correlation ◼ simple linear regression 8 N +1

Correlations in medicine Drinking a glass of red wine per day may decrease your chances of a heart attack a Taking one aspirin per day may decrease your chances of stroke or of a heart attack Eating lots of certain kinds of fish may improve your health and make you smarter a Pregnant women that smoke tend to have low birthweight abies a Taller people tend to weigh more a Animals with large brains tend to be more intelligent The more you study for an exam, the higher the score you are likely to receive

Correlations in medicine ◼ Drinking a glass of red wine per day may decrease your chances of a heart attack. ◼ Taking one aspirin per day may decrease your chances of stroke or of a heart attack. ◼ Eating lots of certain kinds of fish may improve your health and make you smarter. ◼ Pregnant women that smoke tend to have low birthweight babies. ◼ Taller people tend to weigh more ◼ Animals with large brains tend to be more intelligent. ◼ The more you study for an exam, the higher the score you are likely to receive. 9

Model Types. Relationship between variables Deterministic Model: an equation that allow us to fully determine the value of the dependent variable from the values of the independent variables 口S〓R*R Probabilistic Model: a method used to capture the randomness that is part of a real-life process a Weight(Y, kg)Vs. Height (x, cm) 口 For example:18- years-ody=0.8×-69

10 Model Types… Relationship between variables ◼ Deterministic Model: an equation that allow us to fully determine the value of the dependent variable from the values of the independent variables.  S =R*R ◼ Probabilistic Model: a method used to capture the randomness that is part of a real-life process.  Weight(Y,kg) vs. Height (X,cm)/  For example: 18-years-old y=0.8X-69