1. Correlation

2. Let’s study the age and weight of a sample of 10 adults.
Create a scatterplot of the data below.
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. Create a scatterplot of the data below.
Let’s study the height and weight of a sample of 10 adults.
Create a scatterplot of the data below.
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. Identify as having a positive association, a negative association, or no association.+
1. Heights of mothers and 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 NO
Number of hours spent in safety training and the number of accidents that occur -

6. Correlation Coefficient (r)-
A quantitative assessment of the strength & direction of the linear relationship between bivariate, quantitative data
Pearson’s sample correlation is used most
parameter - r (rho)
statistic - r

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

8. Properties of r (correlation coefficient)
legitimate values of r is [-1,1]
Strong correlation No
Correlation
Moderate Correlation
Weak correlation

9. The correlations are the same.
value of r does not depend on the unit of measurement for either variable
x (in mm) y
Find r.
Change to cm & find r.
The correlations are the same.

10. value of r does not depend on which of the two variables is labeled xy
Switch x & y & find r.
The correlations are the same.

11. value of r is non-resistantx y
Find r.
Outliers affect the correlation coefficient

12. r = 0, but has a definite relationship!
value of r is a measure of the extent to which x & y are linearly related
A value of r close to zero does not rule out any strong relationship between x and y.
r = 0, but has a definite relationship!

13. In the 1900’s, it was noticed that as the number of Methodists ministers increased, the imports of rum also increased
The correlation was r = .9999
So does an increase in ministers cause an increase in consumption of rum?

14. Are Ministers Alcoholics?
Number of Methodist Ministers Cuban Rum Imported to Boston
Year in New England (in barrels)
,643
,265
,071
,547
,008
,885
,559
,024
,185
,434
,238
,705

15. Correlation does not imply causation