Correlation

Median HHI and Percent of Households Eligible for Food Stamps

Percent of Households Eligible for Food Stamps and Percent Unemployed

A few words about Scatterplots

• A Scatterplot displays the direction and strength of the association between two sets of quantitative data

• The direction refers to whether there is a positive, negative, or no association between the data

• The association is strong if the dots come close to being in a straight line

• The association is weak if the dots don’t come close to being in a straight line

A number called the correlation measures both the direction and strength of the linear relationship between two related sets of quantitative variables.

Properties of Correlation

• The correlation is written as r

• Correlation requires that both variables be quantitative

• A positive value for r means there is a positive relationship between the variables

• A negative value for r means there is a negative relationship between the variables

• The value of the correlation is always between - 1 and + 1.

• A strong relationship means the correlation is close to either - 1 or + 1

• There can be a strong positive relationship (r is close to 1), or a strong negative relationship (r is close to - 1)

• A weak relationship means the correlation is closer to 0 than to either - 1 or + 1

• The value of r is affected by outliers

Guess the Correlations:

.67 .993 .003 -.975

Excel Formula for Correlation:

=CORREL(array1,array2)

A B

1 3 2

2 4 8

3 7 11

4 3 4

5 8 2

6 5 7

=CORREL(array1,array2)

=CORREL(a1:a6,array2)

=CORREL(a1:a6,b1:b6)

Percent of HH

Eligible for Food Stamps

New AIDS Cases

per 100,000 (2000)

Percent of 35 – 44 y/o

with Bachelor’s

Degree

Percent Unemployed

Percent Unemployed and Not in

Labor Force

Spending per Student

(Grades 1 – 8)

Median HHI (1999) -0.950 -0.659 0.873 -0.895 -0.687 0.147

Percent of HH Eligible for Food Stamps

0.771 -0.875 0.923 0.675 -0.052

New AIDS Cases per 100,000 (2000)

-0.761 0.585 0.268 0.194

Percent of 35 – 44 y/o with Bachelor’s Degree

-0.735 -0.429 0.043

Percent Unemployed 0.666 -0.070

Spending per Student (Grds 1 – 8)

-0.007