AP StatisticsMonday, 26 October 2015

• OBJECTIVE TSW investigate the role of correlation in statistics.

• EVERYONE needs a graphing calculator.

• DUE NOW– Gummi Bear Project (assessment grade) at the beginning

of the period.

• READ– Chapter 6: pp. 150-166

• TODAY’S ASSIGNMENT (due on Tuesday, 10/27/15)

– Chapter 6: pp. 167-170 (3-5 all, 13-16 all)

Chapter 6

Scatterplots, Association, and

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

NO

Now 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?YES

POSITIVE ????????

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 positive association, a negative association, or no 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

-+NO

-

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

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.

r = 0.9963586779

Moderate CorrelationStrong correlation

Properties of r(correlation coefficient)

• Legitimate values of r exist in the interval [-1,1].

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

No Correlation

Weak correlation

The value of r does not depend on the unit of measurement for either variable.

x (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.

0.9181459495

0.9181459495

x 12 15 21 32 26 1924

y 4 7 10 14 9 812

Find r.Switch x & y and find r.

The value of r does not depend on which of the two variables is labeled x and which is labeled y.

The correlations are the same.

The value of r is non-resistant.

x 12 15 21 32 26 1924

y 4 7 10 14 9 822

Find r.Outliers affect the correlation

coefficient

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 there is a definite relationship!

Correlation does not imply causation

Correlation does not imply causation

Correlation does not imply causation

Correlation Coefficient on the Calculator

>> CATALOG >> DiagnosticsOn >> Enter

When you ask for a linear regression equation, the correlation coefficient r is also displayed.

Assignment

• Chapter 6: pp. 167-170 (3-5 all, 13-16 all)–Due tomorrow, Tuesday, 27 October 2015.