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regression

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Medical Statistics (full English class) Shaoqi Rao, PhD School of Public Health Sun Yat-Sen University Slides adapted from Dr. Ji-Qian Fang’s

How does the value of one variable depend on that of another one? ,[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],8.1 Statistical Description of Linear Regression

[object Object],[object Object],[object Object],[object Object],[object Object]

What is regression in statistics? To find out the track of the means 100 120 140 160 180 200 220 100 120 140 160 180 200 220 Father’s height （ cm ） Son’s height (cm)

[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

8.1.2 Regression coefficient and its calculation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 8.1 Calculate the regression equation of the height of son Y on the height of father X .

[object Object],[object Object],[object Object],[object Object],[object Object],8.2 Statistical Inference on Regression 8.2.1 Hypothesis tests

Statistic Standard deviation of regression coefficient Standard deviation of residual

For Example 8.1 p <0.001 . Reject ---- the regression of the son’s height on the father’s height is statistically significant. :  =0, :  ≠0

8.2.1.2 Analysis of variance ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

For Example 8.1 ,[object Object],[object Object],[object Object],[object Object],[object Object]

8.2.2 Determination coefficient For Example 8.1 Determination coefficient: Contribution of regression by % ,[object Object],[object Object],[object Object]

In practice, it is suggested to report the value of determination coefficient after an analysis of regression to describe how good the regression is. ,[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object]

8.3.3 On the basic assumptions ---- LINE ,[object Object],[object Object],[object Object],[object Object]

Summary Regression and Correlation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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