Let the Research Question Choose the Axes
A scatterplot displays paired values for two quantitative variables measured on the same observational units. Which variable belongs on which axis is not a matter of choosing whichever column appears first in a data table. Instead, use the research question: identify the variable being used to help explain or predict another variable, and identify the outcome of interest.
In “Categorical or Quantitative Data: First Decision,” you learned to distinguish quantitative variables from categorical variables. Scatterplots are used to display the relationship between two quantitative variables. This tutorial focuses on deciding how to assign those variables to the axes. The next tutorial, “Constructing a Scatterplot by Hand,” will use that decision to make a plot.
A useful way to decide is to ask: “What outcome is the question asking about?” That outcome is the response variable and goes on the \(y\)-axis. Then ask: “Which other variable is being used to explain or predict that outcome?” That is the explanatory variable and goes on the \(x\)-axis. For example, if the question asks whether hours studied help explain exam score, exam score is the response and hours studied is the explanatory variable.
Write the variable names and units beside the axes. A label such as “Exam score (points)” tells the reader what the response measures; “Hours studied (hours)” identifies the explanatory variable. Units make it easier to understand what each plotted coordinate represents and help prevent accidentally switching the variables.
A Consistent Decision Process
Use the research question rather than the order in which variables happen to be listed. The observational unit also matters: the hours studied and exam score in a pair must refer to the same student, just as each coordinate in a scatterplot must represent one unit.
Identify what one pair of measurements describes, such as one student, one day, or one household.
Look for what the question asks you to explain, predict, or understand. This is the response variable, \(y\).
This is the explanatory variable, \(x\), and goes on the horizontal axis.
Confirm that each \(x\)-value and \(y\)-value belong to the same observational unit, then state each axis label and its units.
Some questions ask only whether two variables are associated, without saying that one explains or predicts the other. In that case, the question does not identify a unique response variable. You may choose a sensible orientation, state it clearly, and keep it consistent. Reversing the axes does not change which observations are paired, but it does change which variable is treated as explanatory and which as response.
Axis placement is a way to organize a question, not evidence that one variable causes the other. In an observational setting, placing a variable on the \(x\)-axis does not make it a cause. Even in an experiment, conclusions about cause and effect depend on the design, such as how treatments were assigned, not simply on which axis a variable occupies.
Worked Example: Hours Studied and Exam Score
A teacher records, for each student, the number of hours the student studied for a unit exam and the student’s score out of 100 points. The research question is: “Do hours studied help explain differences in students’ exam scores?” The following invented data are for six students.
| Student | Hours studied | Exam score (points) |
|---|---|---|
| A | 1 | 62 |
| B | 2 | 68 |
| C | 3 | 72 |
| D | 4 | 81 |
| E | 5 | 84 |
| F | 6 | 91 |
Identify the observational unit. One observational unit is one student. Each student contributes both a study-time measurement and an exam-score measurement.
Choose the response variable. The question asks about differences in exam scores, so exam score is the response variable. It belongs on the vertical \(y\)-axis, labeled “Exam score (points).”
Choose the explanatory variable. The question asks whether hours studied help explain exam scores, so hours studied is the explanatory variable. It belongs on the horizontal \(x\)-axis, labeled “Hours studied (hours).” Student A, for instance, contributes the paired coordinate \((1,62)\), and Student D contributes \((4,81)\).
The wording gives a clear direction: study time is being used to help explain the outcome, exam score. This axis choice does not establish that studying more caused higher scores. Other factors, including prior preparation or study methods, could also be related to the scores.
Worked Example: Outdoor Temperature and Electricity Use
A community analyst records the outdoor temperature at midday and household electricity use over the same day for five households. Electricity use is measured in kilowatt-hours (kWh). The research question is: “Can midday outdoor temperature help predict a household’s daily electricity use?” These invented values illustrate how to assign the axes.
| Household | Midday temperature (°C) | Daily electricity use (kWh) |
|---|---|---|
| 1 | 12 | 24 |
| 2 | 16 | 22 |
| 3 | 20 | 25 |
| 4 | 25 | 31 |
| 5 | 30 | 38 |
Identify the observational unit. One observational unit is a household on the recorded day. The temperature and electricity-use values in each row are paired for that household.
Choose the response variable. The question asks about predicting daily electricity use. Therefore, electricity use is the response variable, \(y\), and belongs on the vertical axis. Label it “Daily electricity use (kWh).”
Choose the explanatory variable. Midday temperature is the proposed predictor, so it is the explanatory variable, \(x\), and belongs on the horizontal axis. Label it “Midday temperature (°C).” Household 4 contributes the coordinate \((25,31)\): 25 degrees Celsius and 31 kWh for that household.
The units matter: the \(x\)-coordinate is a temperature, while the \(y\)-coordinate is an amount of electricity use. The question gives a prediction direction, but does not prove that temperature alone causes differences in electricity use. Household size, heating or cooling systems, and other conditions could also matter.
Worked Example: Commute Distance and Travel Time
A transportation group records commute distance in kilometers and travel time in minutes for five fictional commuters. Its question is: “How is commute distance associated with travel time?” The question asks about association but does not explicitly say that one variable is used to explain or predict the other.
| Commuter | Commute distance (km) | Travel time (minutes) |
|---|---|---|
| A | 3 | 12 |
| B | 5 | 18 |
| C | 8 | 21 |
| D | 10 | 32 |
| E | 14 | 35 |
Identify the observational unit. One observational unit is one commuter. Each distance must remain paired with that commuter’s travel time.
Decide whether the question specifies a direction. It asks how the two variables are associated; it does not designate a response or propose a predictor. So there is no uniquely required axis assignment from the wording alone.
State a consistent choice. For a clear display, choose commute distance as the explanatory variable and place it on the horizontal axis, labeled “Commute distance (km).” Choose travel time as the response variable and place it on the vertical axis, labeled “Travel time (minutes).” For example, Commuter D contributes \((10,32)\).
This is a reasonable convention if distance is being treated as a way to organize or predict travel time. If the group instead chose travel time as \(x\) and distance as \(y\), it should state that choice and keep every pair aligned. The question’s wording should not be misrepresented: it asks about association, rather than asserting that distance explains or causes travel time.
Common Mistakes and AP Exam Tips
- Putting the response on the horizontal axis: The usual convention is explanatory variable on \(x\), response variable on \(y\). Start by identifying the outcome the question asks about.
- Using the order of a table to assign axes: A data table’s first column is not automatically the explanatory variable. Let the research question guide the choice.
- Separating paired values: Keep each unit’s two measurements together. A student’s study time must be paired with that same student’s score; mixing rows changes the data.
- Leaving off units: Label axes with variable names and units, such as “Travel time (minutes),” so a plotted value can be interpreted correctly.
- Claiming that an \(x\)-variable causes the \(y\)-variable: Explanatory means used to explain or predict in the question. It does not, by itself, mean proven cause.
- Insisting every association question has one mandatory orientation: If the wording gives no direction, choose and state a sensible orientation. Do not claim the question specified a response variable when it did not.
For a clear AP response, name the explanatory and response variables in context, connect the choice to the research question, and identify which variable goes on each axis. If the question only asks about association, say that the wording does not specify a direction and state the orientation you choose.
Check Your Understanding
For each question, identify the observational unit when possible and decide which variable belongs on each axis. Explain your choice using the wording of the research question.
- A researcher asks whether weekly exercise time helps explain resting heart rate. What is the explanatory variable, what is the response variable, and which goes on each axis?
- A school records each student’s number of library visits and reading assessment score. The question asks whether visits can help predict scores. Which variable belongs on the \(y\)-axis, and what should the axis label include?
- A parks group asks only whether trail length and visitor count are associated. Does this wording determine a unique response variable? Describe one reasonable axis choice.
- For each of ten devices, a technician records operating temperature and battery life. The question asks whether temperature helps predict battery life. What must remain paired when forming each coordinate?
- Why does placing a variable on the \(x\)-axis not, on its own, show that it causes the variable on the \(y\)-axis?