1. S1: Chapter 6 Correlation Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 21 st November 2013

2. Type of correlation: Weak positive correlation ?? strengthtype Weak negative correlation ?? Strong positive correlation ?? No correlation ? Recap of correlation

3. Recap Variance

4. Covariance We can extend variance to two variables. We might be interested in how one variable varies with another.

5. Covariance Comment on the covariance between the variables. ? ?

6. Covariance Comment on the covariance between the variables. ? ?

7. Covariance

9. Product Moment Correlation Coefficient (PMCC) While the sign (i.e. positive or negative) of the covariance is helpful, the magnitude (i.e. size) is hard to interpret. We can turn our covariance into a correlation coefficient… Dividing by this forces our covariance to be between -1 and 1. We’ll interpret what that means in a second.

10. Product Moment Correlation Coefficient (PMCC) BabyABCDEF 31.133.330.031.535.030.2 363738 40 ? ? ? ? ? ? ? ? ? ?

11. Product Moment Correlation Coefficient (PMCC) ?? ? ? ?? ? ? Quite often the values are given to you in an exam.

12. Let’s do it on our calculators! BabyABCDEF 31.133.330.031.535.030.2 363738 40

13. Interpreting the PMCC We’ve seen the PMCC varies between -1 and 1. means Perfect positive correlation. means No correlation means Perfect negative correlation. ? ? ?

14. Interpreting the PMCC

15. Exercises Page 122 Exercise 6B Q1, 4, 5, 7, 9

16. Limitations of correlation Often there’s a 3 rd variable that explains two others, but the two variables themselves are not connected. Q1: The number of cars on the road has increased, and the number of DVD recorders bought has decreased. Is there a correlation between the two variables? Buying a car does not necessarily mean that you will not buy a DVD recorder, so we cannot say there is a correlation between the two. Q2: Over the past 10 years the memory capacity of personal computers has increased, and so has the average life expectancy of people in the western world. Is there are correlation between these two variables? The two are not connected, but both are due to scientific development over time (i.e. a third variable!) ? ?

17. Effects of coding Unaffected! ? ? ? ? ?

18. Effects of coding

19. Example 102010321028103410231038 320335345355360380 012814318 479111216 We can now just find the PMCC of this new data set, and no further adjustment is needed. ?