Algebra 1 · Unit 10
Write what a scatterplot shows in context, without claiming cause or stretching past the data.
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Say it in context
Replace x and y with the real names: hours, scores, dollars. Keep “tended to” if the cloud is spread out.
Association is not cause
A tight plot does not prove that changing x would change y. A lurking variable can drive both.
Stay inside the data
Do not announce what happens far past the last x-value unless you clearly call it a guess.
Limitations
Name the sample, the missing groups, and any outlier you leaned on.
Write one honest sentence from a clear plot.
Students who practiced more minutes tended to have higher typing speeds in this sample.
That does not by itself prove that extra practice caused the speed.
Answer: positive association in context
Colder days tended to go with higher heating bills in this data.
Answer: negative association
No clear association in this sample.
Answer: no association
No. Association, one night, not an experiment that assigned extra minutes.
Answer: no
Not safely. The class may not represent the city.
Answer: no
No. That is extrapolation far past the data.
Answer: no; extrapolation
Add a limitation, or reject a causal headline.
Ice-cream sales and drowning counts both tended to be higher in warmer months in this data.
Temperature (and more swimming) is a lurking variable. The headline claims cause without an experiment.
Answer: association in summer; not cause
In this random sample of 40, more sleep tended to go with slightly higher quiz scores, but the association was weak.
It describes 9th graders at this school, not a proof that more sleep raises scores.
Answer: weak positive; this school
Report both: with the outlier, weak negative; without it, little trend. Check whether the point is an error.
Answer: report with and without
Bigger fires bring more firefighters and more damage. Fire size lurks.
Answer: lurking fire size
Volunteers at a contest already practice more than a typical student. The strength may not match the whole school.
Answer: volunteer / contest bias
Very small sample. One more point could change the story. Call it tentative.
Answer: too few points
A careful paragraph: pattern, context, cause, window, sample.
Pattern: larger class size tended to go with lower average scores (moderate, negative, roughly linear).
Context: 12 random sections at this school, this spring.
Cause: not shown. Stronger students might be placed in smaller sections.
Window: do not predict a class of 80 if sizes only ran from 18 to 34.
Answer: association, this school, not cause, stay in range
In this year’s data, scores rose with early weeks of practice then leveled off.
Next year’s students, or more weeks than we observed, may not follow the same curve.
Answer: leveled off this year
The random 30. The friends overstate the strength for the grade.
Answer: the random sample
A line is incomplete. Describe a curve, or use a different family, instead of forcing a linear conclusion.
Answer: linear model is poor
The sample and population.
The form, direction, and strength.
That the study did not randomly assign x, so cause is not established.
Answer: sample, pattern, not an experiment
No. Growth can hit limits (housing, jobs). Extrapolation that far is a guess, not a conclusion from the cloud.
Answer: do not extrapolate 30 years
In this sample, more study minutes tended to go with higher quiz scores.
The plot does not prove a 3-point raise for every student, and 10 extra minutes was not randomly assigned.
Answer: association, not a guaranteed raise
A good fit is about the cloud you have.
A school rule is a cause-and-effect decision. That needs an experiment or a much stronger design, plus ethics.
Answer: fit ≠ policy
In this [sample] of [who], [x] and [y] showed a [strength] [direction] [form] association.
Limitation: [not cause / not beyond this x-range / missing group].
Answer: template with limitation
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