1. Chapter 5
Correlation

2. Suppose we found 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.
Suppose we found 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?
Is it positive or negative? Weak or strong? Ht 74 65 77 72 68 60 62 73 61 64 Wt
256
124
320
185
158
129
103
196
110
130

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.+
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 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
How do I determine strength?

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

8. 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.

9. value of r is not changed by any linear transformations
x (in mm) y
Find r.
Change to cm & find r.
Do the following transformations & calculate r
1) 5(x + 14)
2) (y + 30) ÷ 4
The correlations are the same.

10. value of r does not depend on which of the two variables is labeled x
Switch x & y & find r.
Type: LinReg L2, L1
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
Find the correlation for these points: x Y
What does this correlation mean?
Sketch the scatterplot
r = 0, but has a definite relationship!

13. Correlation does not imply causation