TEAS Ready📏 Math · Measurement and Data · Lesson 4 of 7 · 5 min
Two variables: correlation and trends
🔗 Does more sleep go with better test scores? Reading the relationship between two variables is a TEAS favorite.
💡 Key idea
Points rising left to right = positive, falling = negative, scattered = none; and correlation is not causation.
🧠 The idea
The INDEPENDENT VARIABLE is the one that is chosen or changed (hours studied, medication dose); it goes on the x-axis. The DEPENDENT VARIABLE is the one that responds (test score, blood pressure); it goes on the y-axis. A scatter plot shows paired data as points. In a POSITIVE CORRELATION both variables increase together and the points rise from left to right. In a NEGATIVE CORRELATION one increases as the other decreases and the points fall from left to right. With NO CORRELATION the points form no clear pattern. The tighter the points hug a line, the stronger the relationship. To predict, follow the trend: find how much y changes for each step in x and extend it. Remember that correlation alone does not prove that one variable causes the other.
✏️ Worked example
A table pairs hours of practice with free throws made: 1 h → 8, 2 h → 11, 3 h → 14, 4 h → 17. Predict the free throws made after 6 hours.
Step 1: Identify the variables: hours practiced (independent), free throws made (dependent).
Step 2: Find the change per hour: 11 − 8 = 3, 14 − 11 = 3, 17 − 14 = 3. The pattern rises by 3 each hour, a positive correlation.
Step 3: Extend the trend: 5 h → 17 + 3 = 20; 6 h → 20 + 3 = 23.
Answer: about 23 free throws.
📌 Takeaways
- Independent = what you change (x-axis); dependent = what responds (y-axis).
- Positive rises together; negative moves in opposite directions; none has no pattern.
- Predict by extending the constant change along the trend.
📖 Terms in this lesson
Correlation: How two variables change together: positive (both rise), negative (one rises as the other falls) or none; for example, hours studied and test scores often show a positive correlation.
✅ Check yourself
Question 1 of 3
As the number of hours a person exercises each week increases, his resting heart rate tends to decrease. What type of relationship is this?
- Positive correlation
- No correlation
- Negative correlation
- Proof that exercise lowers heart rate
Show the answer and rationale
Answer: C
One variable rises while the other falls, which is a negative correlation. A positive correlation would have both rising, no correlation would show no pattern, and a correlation alone never proves that one variable causes the other.
Question 2 of 3
A researcher gives patients different doses of a drug and measures their blood pressure. What is the independent variable?
- The researcher
- The number of patients
- The blood pressure
- The drug dose
Show the answer and rationale
Answer: D
The dose is the variable the researcher chooses and changes, so it is independent. Blood pressure responds to the dose, making it the dependent variable; the number of patients and the researcher are not the variables being related.
Question 3 of 3
A table shows study hours and scores: 2 h → 70, 3 h → 75, 4 h → 80. If the trend continues, what score is expected after 6 hours?
- 95
- 90
- 85
- 100
Show the answer and rationale
Answer: B
Scores rise 5 points per hour. From 4 h at 80: 5 h → 85, 6 h → 90. Eighty-five is only one more hour, 95 adds an extra step, and 100 assumes 10 points per hour.
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