Two-Variable Data: Models and Scatterplots
Scatterplot questions show up on nearly every test, and the good news is they almost always reward the same handful of moves: plug into a line, read a slope, or judge a correlation. Master those and you bank easy points.
Watch & learn
Short walkthroughs on Two-Variable Data: Models and Scatterplots — ours, plus curated picks. Watch one if a written explanation isn't clicking, or after to reinforce.
Two-variable data means each thing you measure gives you two numbers — like a student's study hours AND their exam score. We plot each person as a single dot at position (x, y). The whole picture of dots is a scatterplot.
Description of the figure:
- The x-axis runs from 0 to 8 and the y-axis from 0 to 110, with grid lines every 1 unit.
- The line rises from left to right.
- It crosses the y-axis at (0, 42) and does not meet the x-axis within the graph.
- It also passes through (2, 59) and (8, 110).
- Marked point: (6, 93).
A line of best fit y = 8.5x + 42: plug in x = 6 hours to predict a score of 93.
Description of the figure:
- The x-axis runs from 0 to 10 and the y-axis from 0 to 30, with grid lines every 1 unit.
- The line falls from left to right.
- It crosses the y-axis at (0, 28) and does not meet the x-axis within the graph.
- It also passes through (10, 5).
- Marked points: intercept at (0, 28) and (10, 5).
- A slope triangle is drawn from (0, 28) to (10, 5), labeled run = 10 and rise = negative 23.
A negative-slope trend line: y falls 2.3 for each +1 in x (a strong negative correlation).
Check your understanding with a question from this topic:
A researcher collected data on the number of hours students studied and their exam scores. The line of best fit for the scatterplot is y = 8.5x + 42, where x is hours studied and y is the predicted exam score. What is the predicted exam score for a student who studied for 6 hours?
Worked examples
A line of best fit models the relationship between the number of practice tests a student takes (x) and their score (y), given by y = 12x + 480. What is the predicted score for a student who takes 5 practice tests?
A scatterplot relates the temperature (in °C) and the number of cups of hot cocoa sold per hour at a cafe. The line of best fit is y = -1.4x + 35. Which statement best interprets the slope in context?
Researchers measured daily screen time (hours) and reported sleep quality (1–10 scale) for 200 people. The correlation coefficient was r = -0.78. Which statement is best supported?
Common pitfalls
The slope is the per-unit rate of change; the intercept is the value when x = 0. If a choice describes 'when x is 0...', it's about b, not the slope. Match the question to the right number.
Even a strong r (like 0.9) only shows the variables move together. Any answer saying one variable causes the other from observational data is wrong on these questions.
Slope describes 'change in y per +1 in x.' Answers that flip the roles ('per additional cup, temperature drops...') are traps — confirm which variable is x.
Key takeaways
Line of best fit is
y = mx + b: plug in x to predict y, or solve for x given y.Slope = change in y for each +1 in x (watch the sign AND the units); intercept = predicted y when x = 0.
Correlation coefficient r ranges from -1 to 1: sign = direction, |r| near 1 = strong, near 0 = weak.
Correlation never proves causation, especially in observational data.
Always check axis units — a hidden 'thousands' or 'percent' changes the answer.
Skill check
10 questions on Two-Variable Data: Models and Scatterplots, from our question bank. Score 70% or better across 10 answers to reach Silver and pass this step.