Section 3.1 ~ Scatterplots
Introduction:
•
This section is going to focus on relationships among several variables for the same group of individuals. In
these relationships, does one variable cause the other variable to change?
•
•
Explanatory Variable:
•
Attempts to explain the observed outcomes
•
Independent variable
Response Variable:
•
Measures an outcome of a study
•
Dependent variable
Example 1 – Effect of Alcohol on Body Temperature
Alcohol has many effects on the body. One effect is a drop in body temperature. To study this effect, researchers gave
several different amounts of alcohol to mice, and then measure the change in the mouse’s body temperature in the 15
minutes after taking the alcohol.

Which variable is the explanatory variable?


Amount of alcohol
Which variable is the response variable?

Change in body temperature
Example 2 – Are SAT Math and Verbal Scores Linked?
Jim wants to know how the median SAT Math and Verbal scores in the 51 states (including District of Columbia) are
related to each other.

Since he is just simply looking to see how they relate to each other, he has two variables, but neither are
explanatory
Suppose Julie looks at the same data and she asks, “Can I predict a state’s median SAT Math score if I know its median
SAT Verbal score?” Can you now determine an explanatory and response variable?

She is treating the Verbal score as the explanatory variable and the Math score as the response variable
**Note – Just by calling one variable explanatory and the other variable response, doesn’t mean there is a cause and
effect relationship. It could also mean that they are closely related and therefore able to be used to make predictions.
Principles That Guide Examination of Data:
•
Although the statistical techniques used to study relations among variables are more complex than onevariable methods from Ch. 1 and 2, the analysis process is the same:
1. Plot the data, then add numerical summaries.
2. Look for overall patterns and deviation from those patterns.
3. When the overall pattern is quite regular, use a compact mathematical model to describe it.
Scatterplots:

Most effective way to display relationship between two
quantitative variables

Shows the relationship between two quantitative variables
measured on the same individuals

Each individual in the data appears as the point in the plot

Plot the _______________ variable on the _______________ axis

Plot the _______________ variable on the _______________ axis.
Examining scatterplots:

Describe the overall pattern of a scatterplot by:

Form – linear, quadratic, logarithmic, etc.

Direction – positive or negative.

Strength of the relationship – weak, moderate, or strong.

An important kind of deviation: is an outlier.

Note any clustering of the data

Variable Association:

Positively associated


Direct Variation – as one variable increases, the other also increases (or decrease-decrease)
Negatively Associated

Inverse Variation – as one variable increases, the other decreases
Tips for drawing scatterplots:
1) Scale the vertical and horizontal axes.
a. Intervals must be uniform
b. Use a symbol to indicate a break in the scale if the scale does not begin at zero
2) Label both axes, and title the graph.
3) If you are given a grid, try to adopt a scale that makes your plot use the whole grid.
Example 3 – Average Degree Days and Natural Gas Consumption
The following table represents the average number of days during the month that are considered heating degree days
and the average amount of natural gas consumed each day during a month, in hundreds of cubic feet. Create a
scatterplot and describe its overall pattern.
Month
Degree-Days
Gas (100 cu. Ft)
Month
Degree-Days
Gas (100 cu. Ft)
Nov.
24
6.3
Nov.
0
1.2
Dec.
51
10.9
Dec.
1
1.2
Jan.
43
8.9
Jan.
6
2.1
Feb.
33
7.5
Feb.
12
3.1
Mar.
26
5.3
Mar.
30
6.4
Apr.
13
4.0
Apr.
32
7.2
May
4
1.7
May
52
11.0
June
0
1.2
June
30
6.9