Math · Problem-Solving and Data Analysis
Two-Variable Data: Models and Scatterplots
A scatterplot compares paired variables. Read the direction and shape of the association, use a model to predict an output, and distinguish an observed value from that prediction.
Read a model's slope in the variables' units
Suppose predicts plant height in centimeters from time in weeks. The slope predicts 3 more centimeters for each additional week. At week 5, the predicted height is centimeters.
The intercept predicts 12 centimeters at week zero. If zero is outside the observed range, that intercept is still part of the equation but may not describe a measured condition.
Calculate residual as actual minus predicted
If the observed height at week 5 is 25 centimeters, the residual is centimeters. The point lies below the model because the prediction is too high by 2.
Keep the order fixed. Predicted minus actual would reverse the sign. A residual of zero means the observation is exactly on the model, not that the height itself is zero.
Match the model to the pattern
A roughly straight cloud of points can support a linear model. A steadily changing ratio, such as outputs doubling over equal input intervals, suggests an exponential model. Curvature in the scatterplot gives a reason to question a straight-line fit.
A strong association means the model follows the observed pattern closely. It does not establish that changing one variable causes the other to change; another variable could influence both.
Limit predictions to what the data support
A model built from measurements over weeks 1 through 8 predicts week 5 within its observed range. Predicting week 50 is extrapolation and needs an assumption that the same relationship continues.
When a question asks which conclusion is supported, check both the direction of the association and the size of the claim. A model can estimate a value without guaranteeing that exact outcome for every observation.
Check your understanding
Try it yourself
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Two-Variable Data: Models and Scatterplots · Worksheet question
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Practice this skill
- Label both axes and the units of the slope.
- Calculate a prediction and one residual by hand.
- Identify whether each prediction is inside or outside the measured range.
Print the two-variable data: models and scatterplots worksheet and worked answers.
Then use a mixed practice module to check whether you can choose this method among other question types.
Source and question labels
The bank label for this guide is "Two-variable data: Models and scatterplots" in Problem-Solving and Data Analysis. The worked examples above are written for this guide.