Algebra 1 · Unit 10
Decide which numerical variables could help explain a situation, and which belong on each axis.
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Explanatory and response
The variable you think might help explain sits on the x-axis. The one you want to understand sits on the y-axis.
Could help, not must cause
A related variable can still be useful even if it is not the only cause. Name what you will measure, not a hidden third thing you cannot see.
Match the question
If the question is about quiz scores, do not collect only favorite color. Collect a numerical score and a numerical partner (minutes studied, hours of sleep).
Lurking variables
Something you did not measure can still drive both axes. Say what else might matter.
Pick which variable belongs on x, which on y.
Hours of study is the input we think might help explain the score.
x = hours, y = quiz score.
Answer: hours on x; score on y
Temperature helps explain sales. x = temperature, y = cups.
Answer: temperature on x
Weeks of training and time.
Answer: weeks of training
Favorite subject is not a numerical explanatory variable for height. Age or parent height would be more reasonable.
Answer: wrong pair
Example: high temperature, or rainfall, or day of week as a number 1–5.
Answer: weather or day index
Yes. Pages could help explain time.
Answer: yes
Choose among several candidates, and name a lurking variable.
Collect minutes studied and hours of sleep — both could reasonably relate to scores.
Pencils and locker number are not explanatory for a quiz in any usual story.
Answer: study minutes and sleep
Example: a holiday week, weather, or a competitor’s sale. Those can move sales without advertising.
Answer: e.g. holiday or weather
Soil type is a category (sand, clay). You need a numerical x such as milliliters of water per day.
Answer: need a numerical x
Hours studied. Texts during the exam may be against the rules and not a variable you should encourage.
Answer: hours studied
Example: weeks left in the semester, or hours the library was open that week.
Answer: need an x
In one class, ages barely vary, so the scatterplot has almost no spread in x.
Answer: too little spread in x
More than one reasonable pair, and a pair that looks related but is not useful.
Useful: temperature, number of beaches open (counts).
Day of year can work as a number 1–365 if seasons matter.
Poor if it is a category: “weekend vs weekday” unless coded, and parking price may be constant so it does not explain changes.
Answer: temperature and a varying count
ID is an arbitrary label. It does not explain scores. A scatterplot would be noise.
Answer: ID is not explanatory
Either might help. They might also be related to each other (a lurking link). Two plots (sleep vs score, phone vs score) show which cloud is tighter.
Answer: either might help; compare clouds
x = mg of caffeine before the test, y = test score.
Lurking: hours of sleep, or who already drinks coffee every day.
Answer: mg vs score; sleep lurks
A classroom (or a section), not a single student, because the y-value is a class average.
Answer: a class
Keep, with care: month 12 to 1 wraps around. A better x might be average temperature that month.
Answer: temperature is cleaner than month
Should not: locker number, last four digits of a phone number.
Could: minutes studied.
Answer: labels vs minutes studied
Make two scatterplots: water vs height, and sunlight hours vs height.
The tighter trend (stronger pattern, clearer form) is the more helpful x — still not proof of cause.
Answer: compare the two scatterplots
More ice time might go with more goals (positive association).
Better players may get both more ice time and more goals — a lurking variable. Association is not by itself a cause.
Answer: association ≠ cause
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