AP Statistics Unit 2 Exploring Two-Variable Data

Topic 2.5: Correlation

Correlation
Video Follow-Along Worksheet
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Learning Objectives: Essential Knowledge:

Key Vocabulary

CorrelationA numerical measure of the direction and strength of a linear relationship between two quantitative variables.
Correlation CoefficientThe value r that summarizes the direction and strength of a linear association.
Positive CorrelationAs x-values increase, y-values tend to increase.
Negative CorrelationAs x-values increase, y-values tend to decrease.
MagnitudeThe distance of r from 0; it is used to describe strength.
Unit-freeHaving no measurement units attached to the numerical value.
Linear AssociationA relationship that follows an approximately straight-line pattern.
Strong CorrelationA correlation with magnitude close to 1.
Weak CorrelationA correlation with magnitude close to 0.
Perfect Linear AssociationA relationship with r = 1 or r = -1.
No Linear AssociationA relationship with r = 0.
CausationA cause-and-effect relationship in which a change in one variable produces a change in another.

Video 1: Correlation and Interpreting r

[0:01 – 5:49]
1. [0:05] Topic 2.5 uses correlation, or the correlation coefficient , to interpret a relationship.
2. [0:16] The lesson focuses on how to calculate , how to it, and what properties of a can be learned from that value alone.
Attendance and Test Score Context [0:31 – 1:15] The video returns to the same sample of 11 students from earlier lessons. School leaders hoped that if they could raise attendance, then test scores might also rise for students facing educational barriers.
3. [1:29] The sample data showed a strong relationship between attendance and exam performance.
4. [2:01] The correlation coefficient r gives the and quantifies the of a linear relationship.
Correlation Coefficient r [2:01 – 2:31]
r = (1 / (n - 1)) Σ [((xi - x̄) / sx)((yi - ȳ) / sy)]
5. [2:10] The most common way to determine r is by using .
6. [2:31] Correlation values span from to , inclusive.
7. [2:59] A negative r value indicates a correlation, meaning as x increases, y tends to .
8. [3:07] A positive r value indicates a correlation, meaning as x increases, y tends to .
9. [3:16] When r is closer to , the correlation is .
10. [3:16] When the magnitude of r is closer to , the correlation is .
11. [3:33] For the attendance data, the calculator gives r = .
12. [3:33] Because r = 0.95 is positive and close to 1, the relationship is very and .
13. [4:28] After attendance initiatives, attendance but test scores stayed .
14. [5:10] A strong positive correlation still does not guarantee that changing attendance will test scores.
15. [5:29] The of r tells the direction of a linear relationship.
16. [5:29] The of r tells the of a linear relationship.
17. [5:29] The correlation coefficient alone does not tell us the of the pattern or any unusual .
18. [5:29] To judge form or unusual features, we must inspect the .
What r Can and Cannot Tell You [5:28 – 5:49]
19. Reflection: How do the sign and magnitude of r help you interpret a linear relationship?
20. Reflection: Why can't correlation by itself prove causation or fully describe a scatterplot?

Exit Ticket

A teacher recorded the number of hours students spent in after-school tutoring and the quiz score each student earned. Technology reports that the correlation is r = 0.89.

Student Hours of Tutoring Quiz Score (%)
A 1 64
B 2 69
C 3 73
D 4 79
E 5 83
F 6 88

(a) Interpret the sign and strength of r in context.

(b) Explain one thing that r alone does not tell you about the scatterplot.

(c) Does this correlation prove that more tutoring caused higher quiz scores? Explain.

(d) State one reason students usually use technology to calculate r.

Class Responses (Esc to close)

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