Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)

Positive correlation

On average, asXgets larger,Ygets
larger; or, asXgets smaller,Ygets
smaller.

Negative correlation

On average, asXgets larger,Ygets
smaller; or asXgets smaller,Ygets
larger.

Perfect

linearity

r = + 1 r = – 1

A positive correlation betweenXandYmeans

that larger values ofX, on average, correspond

with larger values ofY, whereas smaller values

of X correspond with smaller values of Y.

For example, persons who are above mean

height will be, on average, above mean weight,

and persons who are below mean height will

be, on average, below mean weight. This

implies that the correlation between indivi-

duals’ height and weight measurements is pos-

itive. This is not to say that there cannot be

tall people of below average weight or short

people of above average weight. Correlation is

a measure of average, even though there may

be variation among individual observations.

Without any additional knowledge, we would

expect a person 6 ft tall to weigh more than a

person 5 ft tall.

A negative correlation betweenXandYmeans

that larger values ofX, on average, correspond

with smaller values of Y, whereas smaller

values ofXcorrespond with larger values ofY.

An example of negative correlation might be

between hours of exercise per week and body

weight. We would expect, on average, people

who exercise more to weigh less, and con-

versely, people who exercise less to weigh

more. Implicit in this statement is the control

of other variables such as height, age, gender,

and ethnicity.

The possible values of the correlation ofXand

Yrange from negative 1 to positive 1. A corre-

lation of negative 1 implies that there is a per-

fect negative linear relationship betweenXand

Y, whereas a correlation of positive 1 implies

a perfect positive linear relationship between

XandY.

EXAMPLE

Height and weight

Height X

Y

X

(X, Y)

Weight Y

EXAMPLE

Exercise X

Hours of exercise

and body weight

Body Weight Y

Y

X

(X, Y)

Presentation: IV. Covariance and Correlation 501