http://www.ck12.org Chapter 9. Regression and Correlation
9.1 Scatterplots and Linear Correlation
Learning Objectives
- Understand the concept of bivariate data, correlation and the use of scatterplots to display bivariate data.
- Understand when the terms “positive,” “negative” “strong,” and “perfect” apply to correlation between two
variables in a scatterplot graph. - Calculate the linear correlation coefficient and coefficient of determination using technology tools to assist in
the calculations. - Understand properties and common errors of correlation.
Introduction
So far we have learned how to describe the distribution of a single variable and how to perform hypothesis tests that
determine if samples are representative of a population. But what if we notice that two variables seem to be related
to one another and we want to determine the nature of the relationship. For example, we may notice that scores for
two variables – such as verbal SAT score and GPA – are related and that students that have high scores on one appear
to have high scores on another (see table below).
TABLE9.1: A table of verbal SAT values and GPAs for seven students.
Student SAT Score GPA
1 595 3. 4
2 520 3. 2
3 715 3. 9
4 405 2. 3
5 680 3. 9
6 490 2. 5
7 565 3. 5These types of studies are quite common and we can use the concept ofcorrelationto describe the relationship
between variables.
Bivariate Data, Correlation Between Values and the Use of Scatterplots
Correlation measures the relationship betweenbivariate data. In general, bivariate data are data sets with two
observations that are assigned to the same subject. In our example above, we notice that there are two observations
(verbal SAT score and GPA) for each ’subject’ (in this case, a student). Can you think of other scenarios when we
would use bivariate data?
As mentioned, correlation measures the relationship between two variables. If we carefully examine the data in the
example above we notice that those students with high SAT scores tend to have high GPAs and those with low SAT