Chapter 3

Correlation

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

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?

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?

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

Identify as having a positivepositive association, a negativenegative association, or nono association.

1. Heights of mothers & heights of their adult daughters

++

2. Age of a car in years and its current value

3. Weight of a person and calories consumed

4. Height of a person and the person’s birth month

5. Number of hours spent in safety training and the number of accidents that occur

--++NONO

--

Correlation Coefficient (r)-

• A quantitativequantitative assessment of the strength & direction of the linear relationship between bivariate, quantitative data

• Pearson’s sample correlation is used most

• parameter - rho)

• statistic - r

y

i

x

i

s

yy

s

xx

nr

1

1

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

There is a strong, positive, linear relationship between speed limit and average number of accidents per week.

Moderate CorrelationStrong correlation

Properties of r(correlation coefficient)

• legitimate values of r is [-1,1]

0 .5 .8 1-1 -.8 -.5

No Correlation

Weak correlation

•value of r does not depend on the unitunit of measurement for either variablex (in mm) 12 15 21 32 26 19 24

y 4 7 10 14 9 8 12

Find r.

Change to cm & find r.

The correlations are the same.

•value of r does not depend on which of the two variables is

labeled x

x 12 15 21 32 26 19 24y 4 7 10 14 9 8 12

Switch x & y & find r.

The correlations are the same.

•value of r is non-resistantnon-resistant

x 12 15 21 32 26 1924

y 4 7 10 14 9 822

Find r.

Outliers affect the correlation coefficient

•value of r is a measure of the extent to which x & y are linearlylinearly

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 definite relationship!

Minister data:(Data on Elmo)

r = .9999

So does an increase in ministers causecause an increase in consumption of rum?

Correlation does not imply causation

Correlation does not imply causation

Correlation does not Correlation does not imply causationimply causation