1. Simple Linear Regression and Correlation Teaching Assistant: Zuo Xiaoyu Chapter 8

3. Discussion part

5. Table 8-1 psychosis intensity scores and plasma amphetamine levels for 10 chronic amphetamine abusers 475 55 10 350 40 9 200 15 8 425 50 7 400 35 6 450 45 5 150 15 4 250 20 3 300 30 2 150 10 1 Plasma amphetamine mg/ml (X) Psychosis intensity score (Y) patient

8. Procedure

9. Scatter diagram

10. Different types of relation

14. Output and Interpretation Pearson correlation Spearman correlation

17. The direction of correlation? -- positive or negative The strength of correlation? high or not? -- Is the absolute value big enough? Complete correlation : +1 or -1, Understanding the r

23. Y X

24. Output and Interpretation Intercept and slope

26. Output and Interpretation ANOVA result

28. Output and Interpretation R square Hypothesis testing on the regression coefficient

32. Summary of discussion part

38. 3. For bivariate normal distributed variables, regression could be used to interpret correlation: The high determine coefficient indicates the X is closely correlated to Y. 2. The hypothesis testing for correlation coefficient and regression coefficient is equivalent. 1. The correlation coefficient has the same sign as regression coefficient. connection 1.investigate the quantitative dependency relationship between variables 2.prediction 3. variable selection investigate the quantitative association Application Independent variable be a normally distributed random variable. Bivariate normal distribution Pre-requisite Investigate the dependency relationship between the independent and dependent variables. Quantify the relationship between two or more variables. Implication Regression Correlation

42. Heights (cm) of 20 pairs of father and son