Scatter Plot (or Scatter Diagram)

 Business and economic analyses are often concerned about relationships between variables. Do higher SAT mathematics scores predict higher collage GPAs? What is the change in quantity sold as the result of a change in price? How are total sales influenced by total disposable income in a geographic region? Does advertising increase sales? What is the change in infant mortality in developing countries as per capita income increases?

In these examples we notice that one variable may depend to a certain extent on the other variable. For example, a student’s GPA may depend on his or her SAT math score, We then call GPA the dependent variable and label it Y. We call SAT math score the independent variable and label it X. Similarly, we would label the quantity sold as Y and the price of a commodity as X.

To answer these questions, we gather and analyze random samples of data collected from relevant populations.

A scatter diagram insight as the to the relationship that may exist between two variables. We can prepare a scatter plot by locating one point for each pair of two variables that represent an observation in the data set. The scatter plot provides a picture of the data, including the following:

1.    The range of each variable.
2.    The pattern of values over the range
3.    A suggestion as to a possible relationship between the two variables
4.    An indication of outliers (extreme points)

We could prepare scatter plots by plotting individual points on graph paper. However, all modern statistical packages contain routines for preparing scatter plots directly from an electronic data file.

Example: Table below gives the SAT math scores from a test given before admission to college and the GPAs at college graduation for a random sample of 11 students at one small private university. Draw a scatter plot and determine what information it provides.

SAT MATH	450	480	500	520	560	580	590	600	620	650	700
GPA	3.25	2.60	2.88	2.85	3.30	3.10	3.35	3.20	3.50	3.59	3.95

Solution: Using Excel, we obtain the flowing Figure, a scatter plot of the dependent variable, college GPA, and the independent variable, SAT math score. An interesting pattern is the positive upward trend—GPA scores tend to increase directly with increases in SAT math scores. Note also that the relationship does not provide an exact prediction. Some students with low SAT math scores have higher GPA scores than do students with higher SAT math scores. We that the basic pattern indicates that higher entrance scores predict higher grade point averages, but the results are not perfect.