Section 1.2: Using Data to Create Scatterplots
Although a table is useful to display data, it sometimes is better to graph the data, giving a more
visual picture of the situation. To create a graph, first define the variables involved and determine
which variable depends on the other. In many cases this may not be clear. It may be easier to
determine which variable is independent.
Independent variable – input variable, it is generally the value we can choose to determine a result,
also the domain value, usually x
Dependent variable – output variable, it is generally the result we are looking for, also the range
value, usually y.
Scatterplot – A graphical representation of real-world data; consists of a rectangular coordinate
system with independent variable on the horizontal axis and dependent variable on the vertical axis.
There are no lines connected the data until we make an estimate (or regression) that may predict
the outcomes for data not in the table. A scatterplot is also called a statplot on TI calculators.
The points at which a graph crosses the axes are called intercepts. The y-intercept always has an x
value of zero and the x-intercept always has a y value of zero.
Model breakdown – When input values give you outputs that do not make sense in the situation
described in the problem.
Domain – The set of values for the independent variable that results in reasonable output values
with no model breakdown. A domain can be written in interval notation or with inequality symbols.
Range – A set of values for the dependent variable resulting from the given domain values. The
outputs that come from the given domain’s input values. A range should be written in interval
notation or using inequalities.
Example: Create a scatterplot of the data given in the table. The percentage of adults aged 20 years
and over in the United States who are considered obese is given in the table. Source: Centers for
Disease Control, 2008 National Health Interview Survey.
Year
2004
2005
2006
2007
2008
Percent
24.5
25.4
26.4
26.7
26.8
To do this, we choose a suitable starting point for our years. No one wants to use such large
numbers if we can help it, so let t = 0 represent the year 2000. Then we can create a table on the
calculator and plot the points. (See Appendix C-6 through C-8 for the steps required to do this.)
Examples: Concept Investigation Handout – parts 1 – 6.
Example: Use the given graphical model for the population of Russia to answer the following questions.
a) Estimate the population of Russia in 2001.
b) Estimate the year in which the population will be about 140 million people.
c) Estimate the vertical intercept and explain its meaning in regard to the population of Russia.
d) What are a reasonable domain and range for this graphical model? Write your answer using
interval notation.
Example: Malcolm’s Power Pens makes personalized pens for business promotions. The cost to produce
a custom-printed metal pen is given in the table.
Pens
100
200
1000
3000
5000
Cost ($)
90
125
405
1105
1805
a) Define the variables for this problem. Identify which is the independent and which is the
dependent variable. Adjust the data if needed.
b) Create a scatterplot and draw a best-fit line through the data using the regression operation of
your calculator.
c) Using your graphical model, estimate the cost to produce 500 pens.
d) What are a reasonable domain and range for your graphical model? Write your answer using
inequalities.
Example: Use the graph to make estimates.
a) Estimate the vertical intercept. (Also known as the y-intercept.) Write it as a point (x, y).
b) Estimate the horizontal intercept. (Also known as the x-intercept.) Write it as a point (x, y).
c) Estimate the value of x that results in y = 1.
d) Estimate the value of y when x = 3.
Homework: 1, 3 – 6, 15 – 39 odd.