15多元線性回歸

1、Health Statistics,衛(wèi)生統(tǒng)計學(xué),1,Teaching Group,Chuanhua Yu（宇傳華），ProfessorJing Sun （孫靜）， Lecture Lu Ma （馬露） ， Lecture,2,Textbook Book,《衛(wèi)生統(tǒng)計學(xué) 》（第六版），2008.5主編： 方積乾出版：人民衛(wèi)生出版社《衛(wèi)生統(tǒng)計學(xué)學(xué)習(xí)指導(dǎo) 》主編： 方積乾

2、出版：人民衛(wèi)生出版社,3,Reference Books,Bowers David. Medical Statistics from Scratch:An Introduction for Health Professionals (Second Edition). John Wiley & Sons Ltd, 2008.LE CHAP T. Introductory Biostatistics. John Wiley &a

3、mp; Sons Ltd, 2003.Petrie Aviva, Sabin Capoline. Medical Statistics at glance. Blackwell Science Ltd.,2000.方積乾主編.生物醫(yī)學(xué)研究的統(tǒng)計方法. 北京：高等教育出版社，2007.6（ISBN：9787040208412），604頁,4,Method of learning,Preparation Attending Re

4、cording ReviewingPractice,5,Exercise requirements,TranslationWriting in EnglishDetailed processSubmit on time,6,Introduction,緒論,7,Chapter 1,Contents,Statistics & Health statisticsTypes of dataBasic concepts o

5、f statistics,8,New words,StatisticsBiostatisticsHealth statisticsQuantitative dataQualitative dataNumerical dataCategorical data,9,統(tǒng)計學(xué)生物統(tǒng)計學(xué)衛(wèi)生統(tǒng)計學(xué)定量數(shù)據(jù)定性數(shù)據(jù)數(shù)值型數(shù)據(jù)分類型數(shù)據(jù),Continuous dataDiscontinuous dataDiscrete

6、dataBinary dataOrdinal dataNominal dataVariableRandom eventProbability,10,連續(xù)型數(shù)據(jù)非連續(xù)型數(shù)據(jù) 離散型數(shù)據(jù)二分類數(shù)據(jù)順序型數(shù)據(jù)名義型數(shù)據(jù)變量隨機(jī)事件概率,PopulationSampleSample sizeRandom samplingSampling errorParameterStatisticDescripti

7、ve analysisInferential analysis,11,總體樣本樣本量隨機(jī)抽樣抽樣誤差參數(shù)統(tǒng)計量描述分析推斷分析,1,What is statistics?,12,statistics,,Data analysis,13,Basic idea of statistics,Data collection: 100 students 200 students

8、 30 short-sight 40 short-sightInterpretation: 30% abnormal 20% abnormal,Conclusion: The eyesight of students in city Aare bad than those in city B.,Evaluation: 1) Is this conclusion correct?2)

9、What is the reliability (可信度) of the conclusion?,City A City B,Statistics （統(tǒng)計學(xué)）: It is a branch of applied mathematics that refers to the collection and interpretation of data, and evaluation of the reli

10、ability of the conclusions based on the data.,14,Biostatistics （生物統(tǒng)計學(xué)）: It is a branch of the statistics, in which the data are derived from the biological sciences and medicine.,15,Health Statistics It is a branch of

11、the statistics, in which the data are derived from the medical researches about health care, health services, diseases prevention etc.,16,Application of data analysis in the medical research,What is the average birth-wei

12、ght of infants born in Hubei province?Is there any differences of curative effect between two types of medicine?Which risk factors impact on the occurring of stomach cancer? How to predict the likelihood of recovery f

13、rom a disease (prognosis of a disease)?,17,18,Example of detecting a complex relationship between factors,physicalactivity,eating,drinking,smoking,social economic status,enduredglucose,bloodpressure,weight,cholesterol

14、,diabetes,coronary heart disease,environment,life style,endogeneousfactors,diseases,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,19,The position of statistical analysis in medical research,,doctor,patients,,,data,evaluatetreatment,

15、,,statisticalanalysis,improved knowledge,,,feedback,,,An important and necessary course for medicine students,It is an important & useful tool for enhancing the personal ability of medical research;It is also a nec

16、essary subject, like the medical imaging, taken part in an important role for improving the medical science.,20,History of statistics,Beginning in 17th century, it is an application branch of probability theory. Calcul

17、ators (60 decade of 20th) made the basic statistical analysis more applicable.Computers (80 decade of 20th) made the multi-variate statistical analysis more applicable,21,2, Types of data,Data （數(shù)據(jù)）:It is an informatio

18、n derived from the different measuring devices.,22,Source of data,Routine recordsSurveyed recordsExperimental recordsExternal information,23,24,Types of data,data,,,Continuous ( 連續(xù)) Discontinuous (非連續(xù))Discrete (離散),

19、Ordinal ( 順序),Nominal (名義),Quantitative(定量),Qualitative(定性),Numerical(數(shù)值),Categorical(分類),,,Quantitative or numerical data,Quantitative / numerical data （定量 / 數(shù)值數(shù)據(jù)）:It is the data with unit (or scale) and origin .eg,

20、 blood pressure --- continuous white blood cells --- discrete,25,Qualitative or categorical data,（定性 / 分類數(shù)據(jù)）:It is the data without unit (or scale) and origin . eg, sex ---binary (二分類)

21、 likeness ---ordinal (有序多分類) occupation ---nominal (無序多分類),26,3, Basic concepts of statistics,Variable（變量）:It is a set of data observed from different persons, place, things, etc, and it describes

22、 a certain characteristic.,27,28,Data and variable,Event & random event,Event （事件）:Suppose something has k different outcomes, and only one outcome can occurs at a time, then each possible outcome is called as an e

23、vent.,29,eg, tossing a two-sides coin: head or tail.,Random event （隨機(jī)事件）:If the outcome of an event is unknown before trial, then this event is called as a random event.,30,eg, throwing a 6-side die: 1,2,3,4,5,6.,Pro

24、bability （概率）:It is a measure of the likelihood of a random event occurring, using “P” represents it, and 0≤P≤1.,31,32,1) tossing a two-sides coin: head or tail.,,head,P (head facing up) = 1/2,,2) throwing a six-sides

25、 die: 1,2,3,4,5,6 faces.,2,1,3,,P (number ‘6’ facing up) = 1/6,33,Population,population,The blood glucose concentration of female aged 25-39 in Hubei province,The weight ofboys aged 5-10 year olds in Wuhan city.,,Pop

26、ulation （總體）:All collection of measurements about which one wish to draw conclusions.,34,35,Sample,Sample （樣本）:It is a subset of population, and the conclusions about the population can be drawn from it.Sample size （樣

27、本量）: nThe number of individual observations in a sample.,36,37,Random sample,sample,A subset of population,The conclusions about the population can be drawn from the sample.,,,Each member of the population has an equal

28、chance to be selected,The selection of any member from population does not influence the selection of any other member.,Random sampling,,,,equal chance,independent each other,Random sample,Random sample （隨機(jī)樣本）:Each mem

29、ber of the population has an equal chance to be selected and all samples are independent each other.,38,How to draw a random sample?,There are many methods to draw a random sample, for example:Simple random samplingSy

30、stem random samplingClustering random samplingStratified random sampling,39,Table of random numbers,40,10 09 73 25 33 76 52 01 35 16 35 67 23 48 79 80 93 90 11 16 37 24 20 48 05 64 89 47 42 96 24 80 52

31、40 37 20 63 61 04 02 08 42 26 80 53 19 64 50 83 03 23 20 90 25 60 15 35 53 47 78,Example: random sampling 10 students from a class with 70 students.Assign each student in the classroom a unique number from

32、1 to 70.Determine the beginning 2-digits number to be used on the random number table, eg, 1st row and 6th column, the 2-digits number is 76.Read the random numbers from the beginning number, if the random number >

33、;70 or =0, then jump to next number, otherwise, record the number in a paper, if the number is repeated appearing, also jump to next number, do this until a total of 10 different random numbers between 1-70 are recorded

34、.Select the students who has the recorded random number. ie,. The 10 students are those who have the random numbers: 52, 01, 35, 16, 67, 23, 48, 11, 37, 24.,Parameter and statistic,41,population mean,sample mean,,,,,Wha

35、t is a good estimate of parameter?,42,parameter,statistic,unknown,known,,Types of error,43,error,systematic error(系統(tǒng)誤差) ----avoidable,random error（隨機(jī)誤差） ----unavoidable,,,Difference between

36、 true and estimate.,,Sampling error （抽樣誤差）:A type of random error, it is due to the random sampling and the variation between individuals.Random variable（隨機(jī)變量）:A variable measured with random error.Fixed variable（固定變

37、量）:A variable measured without random error.,44,Types of statistical analysis,Descriptive analysis (描述分析) Collect dataInterpretation of data (draw conclusion)Inferential analysis (推斷分析) Evaluate the reliability of t