1. Chapter 21
Linear Modeling

3. Independent Variable is on the x-axis (age)
Dependent Variable is on the y-axis (distance)

7. Correlation A) Direction C) Strength (Think Wentz)
Refers to the relationship or association between two variables.
Characteristics when describing correlation between two variables:
A) Direction
B) Linearity (Think line)
C) Strength (Think Wentz)
D) Outliers
E) Causation

8. Linear Correlation Linear relationships Curvilinear relationships Y YX X Y Y X X
Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall

9. Linear Correlation Strong relationships Weak relationships Y Y X X Y Y
Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall

10. Linear Correlation No relationship Y X Y X
Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall

11. Correlation 11

12. Strength and Direction

13. OUTLIERS
If you have an outlier because of a recording or graphing error, throw it away.
If the outlier is in fact part of the data, keep it.

15. 10 Most Bizarre Correlations

16. 9

17. 8

18. 7

19. 6
M. Night Shyamalan makes bad movies because people don’t buy newspapers.

20. 5

21. Mexican lemon imports prevents highway deaths4
Mexican lemon imports prevents highway deaths

22. Obesity causes national debt to rise3
Obesity causes national debt to rise

23. 2
Facebook also caused the Greek debt crisis

24. 1
Facebook also cancelled out the cholesterol-lowering effects of Justin Bieber

25. Homework: Page 549 (2 – 3)

26. Measuring Correlation

27. Pearson’s correlation coefficient
There are many kinds of correlation coefficients but the most commonly used measure of correlation is the Pearson’s correlation coefficient. (r)
The Pearson r range between -1 to +1.
Sign indicate the direction.
The numerical value indicates the strength.
Perfect correlation : -1 or 1
No correlation: 0
A correlation of zero indicates the value are not linearly related.
However, it is possible they are related in curvilinear fashion.

28. You will need to memorize this and work with it for very long and hard problems.
Just kidding. You can use your calculator to find the “r” value.

29. Positive Correlation

30. Negative Correlation

31. Recall some facts about the correlation coefficient
It tells you whether or not two variables are linearly related to each other.
It tells you whether that relationship is positive or negative.
It indicates the strength of that relationship. 31

32. A warning about the correlation coefficient
Correlation does not imply causation.
To be correlated means the two
variables are related.
Correlation tells you that as one variable changes the other seems to change in a predictable way.
If you want to show one variable causes change in another you need to use a different kind of statistic. 32

33. The correlation coefficient also tells you how much variation in one variable is related to changes in the other variable.
It is NOT a percentage. A correlation coefficient is a ratio. The coefficient of determination, denoted by r2, translates the correlation coefficient into a percentage. 33

34. Example Suppose you compute a correlation coefficient and get r = 0.9.
What does that tell you about the relationship between x and y?
The coefficient of determination is r2 = This tells us that 81% of the variation in y can be explained by using x to predict y in the straight line model. 34

35. Why calculate the coefficient of determination?
It’s easier for most people to understand percents.
For example. if the correlation coefficient on one set of data is r = 0.80 and the correlation coefficient on another set of data is r = you can’t say that the first set of data has a relationship that is twice as strong as the second set (because ”r” IS NOT a percentage). 35

36. Summary
The coefficient of correlation r is a measure of the strength of the linear relationship between two variables x and y.
The coefficient of determination r2 is a measure of percent of variation in one variable that is accounted for by the other variable.

37. Homework: Page 553 (1 – 5)