Scatterplots, Lines of Best Fit, and Correlation

1. Section 1-4 and 1-5
Scatterplots, Lines of Best Fit
... a n d C or re lati on

2. Essential Questions
How do you use scatterplots to solve problems?
How do you use a graphing utility to determine a
line of best fit?
Where you’ll see this:
Retail, education, sports, statistics, insurance

3. Vocabulary
1. Scatterplot:
2. Positive Correlation:
3. Negative Correlation:
4. Line of Best Fit:
5. Trend Line:

4. Vocabulary
1. Scatterplot: Graphing points to show the
relationship between two sets of data
2. Positive Correlation:
3. Negative Correlation:
4. Line of Best Fit:
5. Trend Line:

5. Vocabulary
1. Scatterplot: Graphing points to show the
relationship between two sets of data
2. Positive Correlation: As the horizontal values
increase, so do the vertical values; Has an “uphill”
trend
3. Negative Correlation:
4. Line of Best Fit:
5. Trend Line:

6. Vocabulary
1. Scatterplot: Graphing points to show the
relationship between two sets of data
2. Positive Correlation: As the horizontal values
increase, so do the vertical values; Has an “uphill”
trend
3. Negative Correlation: As the horizontal values
increase, the vertical values decrease; Has a
“downhill” trend
4. Line of Best Fit:
5. Trend Line:

7. Vocabulary
1. Scatterplot: Graphing points to show the
relationship between two sets of data
2. Positive Correlation: As the horizontal values
increase, so do the vertical values; Has an “uphill”
trend
3. Negative Correlation: As the horizontal values
increase, the vertical values decrease; Has a
“downhill” trend
4. Line of Best Fit: A line that comes close to as many
points as possible
5. Trend Line:

8. Vocabulary
1. Scatterplot: Graphing points to show the
relationship between two sets of data
2. Positive Correlation: As the horizontal values
increase, so do the vertical values; Has an “uphill”
trend
3. Negative Correlation: As the horizontal values
increase, the vertical values decrease; Has a
“downhill” trend
4. Line of Best Fit: A line that comes close to as many
points as possible
5. Trend Line: The line of best fit

9. Some Data
The amount of time spent exercising each week
and the resting heart rates on beats per minute
4 h, 60 bpm 3 h, 63 bpm 3.5 h, 67 bpm 4 h, 55 bpm
2 h, 70 bpm 2.5 h, 65 bpm 3 h, 60 bpm 5 h, 50 bpm
4.5 h, 60 bpm 5 h, 65 bpm 4.5 h, 50 bpm 3 h, 70 bpm
5 h, 55 bpm 1 h, 75 bpm 3 h, 55 bpm 4 h, 57 bpm
Create a set of ordered pairs from this data

10. Some Data
The amount of time spent exercising each week
and the resting heart rates on beats per minute
(4, 60) (3, 63) (3.5, 67) (4, 55)
(2, 70) (2.5, 65) (3, 60) (5, 50)
(4.5, 60) (5, 65) (4.5, 50) (3, 70)
(5, 55) (1, 75) (3, 55) (4, 57)

11. Into the TI-83/84

12. Into the TI-83/84

13. Into the TI-83/84

14. Into the TI-83/84

15. Into the TI-83/84

16. Into the TI-83/84

17. Into the TI-83/84

18. Into the TI-83/84

19. Into the TI-83/84

20. Into the TI-83/84

21. Into the TI-83/84

22. Into the TI-83/84

23. Into the TI-83/84

24. Into the TI-83/84

25. Into the TI-83/84

26. Into the TI-83/84

27. Example 1
The following data represents the average time
studying per week in hours with the final grade
earned in math class. Create a scatterplot and put
in a line of best fit, then answer the questions.
(6, 80), (1, 65), (5, 85), (2, 60), (5, 70), (3, 70),
(9, 95), (8, 90), (3, 80), (7, 70), (4, 65), (8, 75),
(4, 80), (7, 85), (9, 85), (10, 95), (1, 75)

28. Example 1

29. Example 1

30. Example 1

31. Example 1

32. Example 1

33. Example 1

34. Example 1

35. Example 1
a. What correlation exists?
b. What is the coefficient of
correlation (r)?
c. If you spent 5 hours a week
studying, what grade would you
expect?

36. Example 1
a. What correlation exists?
b. What is the coefficient of
correlation (r)?
c. If you spent 5 hours a week
studying, what grade would you
expect?

37. Example 1
a. What correlation exists?
Positive
b. What is the coefficient of
correlation (r)?
c. If you spent 5 hours a week
studying, what grade would you
expect?

38. Example 1
a. What correlation exists?
Positive
b. What is the coefficient of
correlation (r)?
c. If you spent 5 hours a week
studying, what grade would you
expect?

39. Example 1
a. What correlation exists?
Positive
b. What is the coefficient of
correlation (r)?
r ≈ .7260615475
c. If you spent 5 hours a week
studying, what grade would you
expect?

40. Example 1
a. What correlation exists?
Positive
b. What is the coefficient of
correlation (r)?
r ≈ .7260615475
c. If you spent 5 hours a week
studying, what grade would you
expect?

41. Example 1
a. What correlation exists?
Positive
b. What is the coefficient of
correlation (r)?
r ≈ .7260615475
c. If you spent 5 hours a week
studying, what grade would you
expect?
About a 77%

42. Question
Respond to this question on edmodo:
How strong should a correlation be in order to
show a strong relationship?

43. Problem Set

44. Problem Set
p. 22 #1-4, 7-12; p. 27 #1-10
“We have, I fear, confused power with greatness.”
- Stewart L. Udall