Unit 3Section 10-3

10-3: Correlation Correlation– statistical method used to

determine whether a relationship between variables exists.

The correlation coefficient is used to determine the strength of the relationship between two variables.

The method we will be using for finding this value is the Pearson product moment correlation coefficient (PPMC).

Correlation coefficient–measures the strength and direction of a linear relationship between two variables.

Symbol for sample correlation coefficient: r Symbol for population correlation coefficient: ρ

The values of the correlation coefficient range from -1 to +1. If the value is close to +1 the variables have a strong

positive relationship. If the value is close to -1 the variables have a strong

negative relationship. If the value is close to 0, the variables have no

relationship or a weak relationship.

Section 10-3

Formula for the Correlation Coefficient (r)

n is the number of data pairs

Section 10-3

Constructing a Scatter Plot Compute the value of the correlation coefficient

for the data obtained in the study of age and blood pressure given below:

Subject Age (x) Pressure (y)

A 43 128

B 48 120

C 56 135

D 61 143

E 67 141

F 70 152

Section 10-3

Table Set Up:

Section 10-3

Subject x y xy x2 y2

The correlation coefficient suggested a strong positive relationship between age and blood pressure

Section 10-3

Constructing a Scatter Plot

Construct a scatter plot for the data obtained in a study of the number of absences and the final grades of seven randomly selected students from a statistics class.

Subject # of Absences (x)

Final Grade (y)

A 6 82

B 2 86

C 15 43

D 9 74

E 12 58

F 5 90

G 8 78

Section 10-3Section 10-3

The correlation coefficient suggested a strong negative relationship between the student’s final grade and the number of absences.

i.e. the larger the number of absences, the lower the grade

Section 10-3

Constructing a Scatter Plot Construct a scatter plot for the data obtained in a

study on the number of hours that nine people exercise each week and the amount of milk (in ounces) each person consumes per week.

Subject Hours (x) Amount (y)

A 3 48

B 0 8

C 2 32

D 5 64

E 8 10

F 5 32

G 10 56

H 2 72

I 1 48

Section 10-3

The value of r indicated a very weak positive relationship between the variables.

Section 10-3

Homework: Read and take notes on Section 10.4

(pg 544 – 554)