Lesson 4 of 6 · Problem-solving and data analysis

Two-variable data: models and scatterplots

7 min read · about 1 h 10 min with practice3 quick checks≈1% of the testCore

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Scatterplot and model questions ask you to read a line or curve of best fit, interpret its slope, intercept or growth factor in context, compare actual and predicted values, and decide whether data are linear or exponential. They are usually quick points, but a single misread word (“predicted,” “per pound,” “percent”) decides the answer.

By the end you’ll be able to

Interpret the slope and intercept of a line of best fit in context
Use a model to make predictions and compute the difference between actual and predicted values
Choose between linear, quadratic and exponential models for a data set
Describe the association in a scatterplot (direction, strength, form)

What the exam asks

Expect about one question per test, often with a figure and usually in context. The main types are:

Predict from a model: read the line on a scatterplot, or substitute into an equation such as $y = -1.8x + 212$ .
Interpret a model: “What is the best interpretation of the slope/of 1.06/of 22,300 in this context?”
Actual versus predicted: “How much greater is the actual value than the predicted value?” or “For how many data points is the actual value greater than predicted?”
Choose the equation of a line or exponential curve of best fit from a graph.
Choose the model type: increasing or decreasing, and linear, exponential or (occasionally) quadratic, from a table or scatterplot.
Describe an association by direction, form and strength.

Core ideas

Describing a scatterplot

Feature	Question to ask	Words used
Direction	As increases, does tend to increase or decrease?

Check your understanding

3 questions on two-variable data: models and scatterplots. Every option is explained once you answer.

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Flashcards

The first 3 of 11 cards for this topic. Sign in and finish the lesson to review them with spaced repetition.

PromptCard 1 of 3

How do you interpret the slope of a line of best fit in context?

x

x

Pattern over equal steps in $x$	Model
Constant difference in $y$	Linear, $y = mx + b$
Constant ratio in $y$	Exponential, $y = a(b)^x$

Feature on the graph	What it fixes
Opens down (an arch) or up (a cup)	$a < 0$ or $a > 0$
Where the curve crosses the $y$ -axis	$c$
The $x$ -coordinate of the peak or low point	$-\frac{b}{2a}$

Two-variable data: models and scatterplots

By the end you’ll be able to

What the exam asks

Core ideas

Describing a scatterplot

Check your understanding

Flashcards

Lines of best fit

Actual versus predicted (residuals)

Linear versus exponential models

Quadratic curves of best fit

Worked examples

Exam technique

Common mistakes

Quick recap

By the end you’ll be able to

What the exam asks

Core ideas

Describing a scatterplot

vii.Check your understanding

viii.Flashcards

Lines of best fit

Actual versus predicted (residuals)

Linear versus exponential models

Quadratic curves of best fit

Worked examples

Exam technique

Common mistakes

Quick recap

Check your understanding

Flashcards