CH09 linear regression and correlation.ppt

Chapter 9
Linear Regression and Correlation
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Bivariate quantitative data:
Population: finite and infinite paired variable values
Sample: n observations on the explanatory and the response variable y randomly sampled from population
(X1,Y1), (X2,Y2), …, (Xn,Yn)
Objective: study the quantitative relationship between X and Y
Method: regression and correlation
Simple ,basic —— linear regression ,linear correlation
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Content

1. Linear regression
2. Linear correlation
3. Rank correlation
4. Curve fitting
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Historic background:
19th century
British anthropologist
correlation and coefficient of correlation
statistician
Karl Pearson found:
There is the linear relationship between the height of the sons (X,inch) and height of fathers (Y,inch).
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That is to say, the height of the sons of the tall fathers do not sure to be taller, while their height maybe shorter than their fathers. However, the height of short father’s son do not sure to be shorter, while they maybe taller than their fathers’ level . Galton call this phenomenon of race steady tendency as regression.
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Now, “regression ” has became the statistic term which show the quantitative dependency between the variables, and formed some new statistic concepts such as the “regression equation” and “regression coefficient”.
For example :
study the relationship between the blood sugar and insulin level .
study the relationship between the the age and the weight of children.
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linear regression
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concepts
Objective: study the dependency between the dependent variable Y and the independent variable X.
Feature: statistic relationship.
relationship between the means of the X and Y
Differ from the functional relationship between
X and Y in general mathmatics
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Example 9-1 : A endemic disease institute has investigated urine creatinine concentrations(mmol/24h) of eight health children , in table 9-1. Please estimate the regres