Show correlation with a line of best fit

Example:

Tracking patterns in human diseases

The US Center for Disease Control (CDC) keeps track of reported cases of many kinds of diseases in the US population. Their mission is to understand the diseases and to prevent or reduce the threats they pose to people. CDC scientists are especially interested in understanding cancer rates, and how strongly different kinds of cancer are correlated with environmental factors such as smoking.

Two questions about lung and skin cancer:

1. Is lung cancer rate correlated with smoking rate? 2. Is melanoma (skin cancer) rate correlated with smoking rate?

Data source: the US Center for Disease Control

Plot the data in a graph that displays the evidence needed to answer each question.

(Make two graphs, one for each question).

Some graphing prompts (if needed):

•What kind of question is being asked? (Use GCC)

• What kind of graph will you use? (Why?)

• What two numeric factors are you analyzing?• Which factor will you put on which axis? (Why?)

• What will each dot represent?

1. Is lung cancer rate correlated with smoking rate?

2. Is melanoma (skin cancer) rate correlated with smoking rate?

Strong positive correlation No correlation

The higher the smoking rate, the higher incidence of lung cancer

The points don’t fall close to a line. Skin cancer seems unrelated to smoking rates.

Lung cancer rate vs. smoking rate Melanoma rate vs. smoking rate

The arrangement of the points shows • How strong the correlation is • Whether the correlation is positive or negative

________________

Positive correlation: one variable is HIGH and the other is also HIGH

“The water temperatures at high and low tides are positively correlated”

Wat

er t

empe

ratu

re a

t lo

w t

ide

Water temperature at high tide

Negative correlation: one variable is HIGH and the other is LOW

The maximum wind speed of a hurricane is negatively correlated with its minimum barometric pressure.

Minimum barometric pressure

Max

imum

win

d sp

eed

Hurricanes

No correlation: Data points are scattered and don’t form a line.

The rate of skin cancer (melanoma) is not correlated with smoking rate.