1. Lesson 4.7 – Interpreting the Correlation Coefficient and Distinguishing between Correlation & Causation
EQs: How do you calculate the correlation coefficient? What is the difference between correlation and causation? (S. ID. 8 & 9)
Vocabulary: correlation, correlation coefficient, strong/weak positive, strong/weak negative
4.3.2: Calculating and Interpreting the Correlation Coefficient

2. Think-Pair-Share
With your partner, come up with an example of two things that affect each other (ex. Studying for a test and your test grade) and two things that do not affect each other (ex. Rolling a die and drawing a card from a deck).
4.3.2: Calculating and Interpreting the Correlation Coefficient

3. Vocabulary
A correlation is a relationship between two events, such as x and y, where a change in one event implies a change in another event.
The correlation coefficient, r, is a quantity that allows us to determine how strong this relationship is between two events. It is a value that ranges from –1 to 1.
4.3.2: Calculating and Interpreting the Correlation Coefficient

4. Correlation Coefficient (r-value)
The correlation coefficient only assesses the strength of a linear relationship between two variables.
The correlation coefficient does not assess causation—that one event causes the other.
.51 to 1
0 to .50
-.51 to -1
0 to -.50
4.3.2: Calculating and Interpreting the Correlation Coefficient

5. Correlation vs. Causation
Correlation does not imply causation, or that a change in one event causes the change in the second event.
If a change in one event is responsible for a change in another event, the two events have a casual relationship, or causation.
Outside factors may influence and explain a strong correlation between two events.
4.3.2: Calculating and Interpreting the Correlation Coefficient

6. Let’s Practice! For each scatter plot identify the correlation type and coefficient.
4.3.2: Calculating and Interpreting the Correlation Coefficient

7. Guided Practice Example 1
An education research team is interested in determining if there is a relationship between a student’s vocabulary and how frequently the student reads books. The team gives 20 students a 100-question vocabulary test, and asks students to record how many books they read in the past year. The results are in the table on the next slide. Is there a linear relationship between the number of books read and test scores? Use the correlation coefficient, r, to explain your answer.
4.3.2: Calculating and Interpreting the Correlation Coefficient

8. Guided Practice: Example 1, continued
Books read
Test score 12 23 5 8 3 15 30 19 14 36 9 56 1 13 63 25 4 6 16 78 2 42 7
4.3.2: Calculating and Interpreting the Correlation Coefficient

9. Guided Practice: Example 1, continued
Create a scatter plot of the data.
Let the x-axis represent books read and the y-axis represent test score.
Test score
Books read
4.3.2: Calculating and Interpreting the Correlation Coefficient

10. Guided Practice: Example 1, continued
Describe the relationship between the data using the graphical representation.
It appears that the higher scores were from students who read more books, but the data does not appear to lie on a line. There is not a strong linear relationship between the two events.
Test score
Books read
4.3.2: Calculating and Interpreting the Correlation Coefficient

11. ✔ Guided Practice: Example 1, continued
Calculate the correlation coefficient on your scientific calculator. Refer to the steps in the Key Concepts section.
The correlation coefficient, r, is approximately 0.48.
Use the correlation coefficient to describe the strength of the relationship between the data.
A correlation coefficient of 1 indicates a strong positive correlation, and a correlation of 0 indicates no correlation. A correlation coefficient of 0.48 is about halfway between 1 and 0, and indicates that there is a weak positive linear relationship between the number of books a student read in the
past year and his or her score on the
vocabulary test. ✔
4.3.2: Calculating and Interpreting the Correlation Coefficient

12. Guided Practice: Example 1, continued
5. Consider the casual relationship between the two events. Determine if it is likely that the number of books read is responsible for the vocabulary test score.
Since reading broadens your vocabulary, and although there are other factors related to test performance, it is likely that there is a casual relationship between the number of books read and the vocabulary test score.
4.3.2: Calculating and Interpreting the Correlation Coefficient

13. Guided Practice Example 2
Alex coaches basketball, and wants to know if there is a relationship between height and free throw shooting percentage. Free throw shooting percentage is the number of free throw shots completed divided by the number of free throws shots attempted:
Alex takes some notes on the players in his team, and records his results in the tables on the next two slides.
4.3.2: Calculating and Interpreting the Correlation Coefficient

14. Guided Practice: Example 2, continued
Height in inches
Free throw % 75 28 76 25 22 70 42 67 30 72 47 80 6 79 24 71 43 69 23 40 27 10
4.3.2: Calculating and Interpreting the Correlation Coefficient

15. Guided Practice: Example 2, continued
Height in inches
Free throw % 76 33 75 13 25 71 30 67 54 68 29 79 5 14 55 78
4.3.2: Calculating and Interpreting the Correlation Coefficient

16. Guided Practice: Example 2, continued
Create a scatter plot of the data.
Let the x-axis represent height in inches and the y- axis represent free throw shooting percentage.
Free throw percentage
Height in inches
4.3.2: Calculating and Interpreting the Correlation Coefficient

17. Guided Practice: Example 2, continued
Describe the relationship between the data using the graphical representation.
Free throw percentage
Height in inches
As height increases,
free throw shooting
Percentage decreases.
It appears that there is a
weak negative linear
correlation between the
two events.
4.3.2: Calculating and Interpreting the Correlation Coefficient

18. Guided Practice: Example 2, continued
Calculate the correlation coefficient on your scientific calculator. Refer to the steps in the previous slides.
The correlation coefficient, r, is approximately
Use the correlation coefficient to describe the strength of the relationship between the data.
A correlation coefficient of –1 indicates a strong negative correlation, and a correlation of 0 indicates no correlation. A correlation coefficient of –0.727 is close to –1, and indicates that there is a strong negative linear relationship between height and free throw percentage.
4.3.2: Calculating and Interpreting the Correlation Coefficient

19. ✔ Guided Practice: Example 2, continued
5. Consider the casual relationship, causation, between the two events. Determine if it is likely that height is responsible for the decrease in free throw shooting percentage.
Even if there is a correlation between height and free throw percentage, it is not likely that height causes a basketball player to have more difficulty making free throw shots. ✔
4.3.2: Calculating and Interpreting the Correlation Coefficient

20. You Try!
Caitlyn thinks that there may be a relationship between class size and student performance on standardized tests. She tracks the average test performance of students from 20 different classes, and notes the number of students in each class in the table on the next slide. Is there a linear relationship between class size and average test score? Use the correlation coefficient, r, to explain your answer.
4.3.2: Calculating and Interpreting the Correlation Coefficient

21. You Try! Class size Avg. test score 26 28 32 33 36 25 27 30 29 21 1938 23 41 34 17 43 37 14 42 39 31
4.3.2: Calculating and Interpreting the Correlation Coefficient

22. You Try! Average test score Number of students
4.3.2: Calculating and Interpreting the Correlation Coefficient

23. You Try!
Describe the relationship between the data using the graphical representation.
As the class size increases, the average test score decreases. It appears that there is a linear relationship with a negative slope between the two variables.
4.3.2: Calculating and Interpreting the Correlation Coefficient

24. You Try!
Calculate the correlation coefficient on your graphing calculator. Refer to the steps in the Key Concepts section.
The correlation coefficient, r, is approximately
–0.84.
4.3.2: Calculating and Interpreting the Correlation Coefficient

25. You Try!
Use the correlation coefficient to describe the strength of the relationship between the data.
A correlation coefficient of –1 indicates a strong negative correlation, and a correlation of 0 indicates no correlation. A correlation coefficient of –0.84 is close to –1, and indicates that there is a strong negative linear relationship between class size
and average test score.
4.3.2: Calculating and Interpreting the Correlation Coefficient

26. You Try!
5. Determine if it is likely that class size is responsible for performance on standardized tests.
Smaller class sizes allow teachers to give each student more attention, however, other factors are related to test performance. But we cannot say that smaller class sizes are directly related to higher performance on standardized tests. Students perform differently on tests regardless of class size. ✔
4.3.2: Calculating and Interpreting the Correlation Coefficient

27. List 3 things you learned this lesson.
3-2-1
List 3 things you learned this lesson.
List 2 examples of correlation/causation.
List 1 question you still have.
4.3.2: Calculating and Interpreting the Correlation Coefficient