Cogito
Probability and Statistics · Chapter 2 · Lesson 3
Scatterplots and Correlation
Two variables at once.
12 problems · about 22 minutes · TEKS P.S.1.E, S-ID.C.9
What this lesson teaches
The student interprets scatterplots, describes correlation, and distinguishes correlation from causation.
- Describe a scatterplot by direction, form and strength.
- r runs from −1 to 1 and measures only straight-line association.
- Correlation never establishes causation on its own.
Warm Up
Straightforward practice. Get the method working first.
5 problemsr = −0.88. Is the relationship strong or weak? 1 strong, 2 weak.
Answer 1
Why Strong, and negative.
What is a lurking variable?
Answer A hidden third factor driving both variables.
Why A hidden third factor.
What is the largest value r can take?
Answer 1
Why A perfect rising line.
What is the smallest value r can take?
Answer -1
Why A perfect falling line.
r = 0.05. Strong or weak linear relationship? 1 strong, 2 weak.
Answer 2
Why Close to zero.
Build It Up
The same ideas with more to keep track of.
3 problemsr = −0.95. Strong or weak? 1 strong, 2 weak.
Answer 1
Why Size, not sign, gives strength.
A perfect U-shaped relationship can have r near zero. True? 1 yes, 0 no.
Answer 1
Why r only measures straightness.
What kind of study can establish causation? 1 observational, 2 controlled experiment.
Answer 2
Why Only one assigns treatments.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsWhich must be reported when describing a scatterplot?
Answer Direction; Form; Strength
Why A scatterplot cannot report a cause.
r = 0.9 between shoe size and reading level in children. Does shoe size cause reading? 1 yes, 0 no.
Answer 0
Why Age drives both.
The Sign: As one variable rises the other falls. Is r positive or negative? 1 positive, 2 negative.
Answer 2
Why Negative.
The Ice Cream: Ice cream sales and drownings both rise in summer. Does one cause the other? 1 for yes, 0 for no.
Answer 0
Why No. Hot weather is a lurking variable.