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regression

Formation

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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Ch8regressionrevbyrao 091127020047 Phpapp02

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

3. Chapter 8 Linear Regression

7. 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)

10.

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

12.

13.

14. Statistic Standard deviation of regression coefficient Standard deviation of residual

15. 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

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