1. Chapter 5
Correlation

2. Suppose we found the age and weight of a sample of 10 adults.
Create a scatterplot of the data.
Is there any relationship between the age and weight of these adults?
Age 24 30 41 28 50 46 49 35 20 39 Wt
256
124
320
185
158
129
103
196
110
130

3. Suppose we found the height and weight of a sample of 10 adults.
Create a scatterplot of the data.
Is there any relationship between the height and weight of these adults? Ht 74 65 77 72 68 60 62 73 61 64 Wt
256
124
320
185
158
129
103
196
110
130
Is it positive or negative? Weak or strong?

4. The farther away from a straight line, the weaker the relationship
The closer the points in a scatterplot are to a straight line, the stronger the relationship
The farther away from a straight line, the weaker the relationship

5. Positive relationship, negative relationship, or no relationship?+
1. Heights of mothers & heights of their adult daughters -
Age of a car in years and its current value +
Weight of a person and calories consumed
Height of a person and the person’s birth month
None
Number of hours spent in safety training and the number of accidents that occur -

6. Correlation Coefficient (r)
Measures strength & direction of a linear relationship
Used for bivariate numerical data

7. Calculate r. Interpret it in context.
Speed Limit (mph) 55 50 45 40 30 20
Avg. # of accidents (weekly) 28 25 21 17 11 6
Calculate r. Interpret it in context.
There is a strong, positive, linear relationship between speed limit and average number of accidents per week.

8. Properties of r Legitimate values of r: from -1 to 1
Strong correlation No
Correlation
Moderate Correlation
Weak correlation

9.  r does not depend on units
x (in mm) y
Find r.
Change x to cm & find r.
The correlations are the same.
 r does not depend on units

10.  r does not depend on which variable is x and which is y
Switch x & y, then find r.
The correlations are the same.
 r does not depend on which variable is x and which is y

11. Outliers affect the correlation coefficientx y
Find r.
Outliers affect the correlation coefficient
 r is non-resistant

12.  r only measures how well x & y are linearly related
r = 0, but there's a definite relationship!
 r only measures how well x & y are linearly related

13. Do Methodist ministers drink a lot of Cuban rum?

14. Methodist Ministers Barrels of Cuban Rum
Year in New England Imported to Boston
,643
,265
,071
,547
,008
,885
,559
,024
,185
,434
,238
,705

15. The correlation coefficient for this relationship is r =. 999986
The correlation coefficient for this relationship is r = What can we conclude?

16. Did the increase in Methodist ministers cause the increase in consumption of Cuban rum?

17. Study suggests attending religious services sharply cuts risk of death

18. Facebook Users Get Worse Grades in College

19. TV raises blood pressure in obese kids

20. Deep-voiced men have more kids

21. Height Affects How People Perceive Their Quality Of Life

22. Eating pizza cuts cancer risk

23. Diet of fish can prevent teen violence

24. Happiness wards off heart disease, study suggests

25. Sugar Rush… to Prison? Study Says Lots of Candy Could Lead to Violence

26. Correlation does not imply causation