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Integrated Math 2 Section 1-4 and 1-5

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Scatterplots, Lines of Best Fit, and Correlation

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Integrated Math 2 Section 1-4 and 1-5

  1. 1. Section 1-4 and 1-5 Scatterplots, Lines of Best Fit ... a n d C or re lati on
  2. 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. 3. Vocabulary 1. Scatterplot: 2. Positive Correlation: 3. Negative Correlation: 4. Line of Best Fit: 5. Trend Line:
  4. 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. 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. 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. 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. 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. 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. 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. 11. Into the TI-83/84
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  27. 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. 28. Example 1
  29. 29. Example 1
  30. 30. Example 1
  31. 31. Example 1
  32. 32. Example 1
  33. 33. Example 1
  34. 34. Example 1
  35. 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. 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. 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. 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. 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. 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. 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. 42. Question Respond to this question on edmodo: How strong should a correlation be in order to show a strong relationship?
  43. 43. Problem Set
  44. 44. Problem Set p. 22 #1-4, 7-12; p. 27 #1-10 “We have, I fear, confused power with greatness.” - Stewart L. Udall

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