CK-12-Pre-Calculus Concepts

15.7. Linear Correlation http://www.ck12.org

15.7 Linear Correlation

Here you will begin to work with bivariate data as you learn about linear correlation, correlation coefficients, and
regression.
Statistics is largely concerned with how a change in one variable relates to changes in a second variable. Bivariate
data is two lists of data that are paired up. Is there any relationship between the following data? If there is, does it
mean that doctors cause cancer?

TABLE15.11:

Number

of

Doctors

27 30 36 60 81 90 156 221 347

Cancer

Rate

0.02 0.07 0.16 0.20 0.43 0.87 1.21 2.80 3.91

Watch This

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/62997

http://www.youtube.com/watch?v=ROpbdO-gRUo Khan Academy: Correlation vs. Causality

Guidance

Ascatterplotcreates an(x,y)point from each data pair. When making a scatterplot, you can try to assign the
independent variable toxand the dependent variable toy; however, it will often not be obvious which variable is the
dependent variable, so you will just have to pick one.
Once you plot the data and zoom appropriately you will see the points scattered about. Sometimes there will be
a clear linear relationship and sometimes it will appear random. Thecorrelation coefficient,r, is a number that
quantifies two aspects of the relationship between the data:

• The correlation coefficient is either negative, zero or positive. This tells you whether the data is negatively
  correlated, uncorrelated or positively correlated.


• The correlation coefficient is a number between− 1 ≤r≤1 indicating the strength of correlation. Ifr= 1
  orr=−1 then the data is perfectly linear. Note that a perfectly linear relationship includes lines with slopes
  other than 1.

Consider the examples below to see what different correlation coefficients will look like in data: