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Oct. 12 - Scatter Plots Day 3

algebra 1<br>middle school & high school math

cocoore
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Oct. 12 - Scatter Plots Day 3

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  1. train your brain day! 10.12.22 OUTCOME(s): Sign into the Desmos Graphing Calculator. Pick up the warm-up and complete it. Agenda: • Warm-up • Practice Predictions • Lesson: Residuals I can determine the residual for a given data point. Pencil, Calculator, Notebook, Chromebook

  2. Scatter Plots and Lines of Best Fit Day 3 - Residuals

  3. Warm Up - Linear Regression Models Name: Date: Period: Use the Desmos Graphing Calculator to answer the following. 1. What is the linear regression equation (rounded to tenths)? 2. What is the slope and what does it mean in context? 3. What is the y-intercept and what does it mean in context? 4. What is the correlation coefficient (rounded to nearest hundredth)? 5. What does the correlation coefficient tell us about this data? 6. What is the predicted salary for someone with 10 years experience? 7. It that an example of interpolation or extrapolation? Why?

  4. Warm Up - Linear Regression Models Name: Date: Period: Use the Desmos Graphing Calculator to answer the following. 1. What is the linear regression equation (rounded to tenths)? y = 4.8x + 9.2 2. What is the slope and what does it mean in context? 3. What is the y-intercept and what does it mean in context? 4. What is the correlation coefficient (rounded to nearest hundredth)? 5. What does the correlation coefficient tell us about this data? 6. What is the predicted salary for someone with 10 years experience? 7. It that an example of interpolation or extrapolation? Why?

  5. Warm Up - Linear Regression Models Name: Date: Period: Use the Desmos Graphing Calculator to answer the following. 1. What is the linear regression equation (rounded to tenths)? y = 4.8x + 9.2 2. What is the slope and what does it mean in context? The slope is 4.8. It means that the salary goes up 4.8 thousand dollars each year. In other words, the salary increases $4800 per year. 3. What is the y-intercept and what does it mean in context? 4. What is the correlation coefficient (rounded to nearest hundredth)? 5. What does the correlation coefficient tell us about this data? 6. What is the predicted salary for someone with 10 years experience? 7. It that an example of interpolation or extrapolation? Why?

  6. Warm Up - Linear Regression Models Name: Date: Period: Use the Desmos Graphing Calculator to answer the following. 1. What is the linear regression equation (rounded to tenths)? y = 4.8x + 9.2 2. What is the slope and what does it mean in context? The slope is 4.8. It means that the salary goes up 4.8 thousand dollars each year. In other words, the salary increases $4800 per year. 3. What is the y-intercept and what does it mean in context? The y-intercept is 9.2. It means that the starting salary was 9.2 thousand dollars. In other words, the starting salary was $9200. 4. What is the correlation coefficient (rounded to nearest hundredth)? 5. What does the correlation coefficient tell us about this data? 6. What is the predicted salary for someone with 10 years experience? 7. It that an example of interpolation or extrapolation? Why?

  7. Warm Up - Linear Regression Models Name: Date: Period: Use the Desmos Graphing Calculator to answer the following. 1. What is the linear regression equation (rounded to tenths)? y = 4.8x + 9.2 2. What is the slope and what does it mean in context? The slope is 4.8. It means that the salary goes up 4.8 thousand dollars each year. In other words, the salary increases $4800 per year. 3. What is the y-intercept and what does it mean in context? The y-intercept is 9.2. It means that the starting salary was 9.2 thousand dollars. In other words, the starting salary was $9200. 4. What is the correlation coefficient (rounded to nearest hundredth)? The correlation coefficient is 0.98. 5. What does the correlation coefficient tell us about this data? 6. What is the predicted salary for someone with 10 years experience? 7. It that an example of interpolation or extrapolation? Why?

  8. Warm Up - Linear Regression Models Name: Date: Period: Use the Desmos Graphing Calculator to answer the following. 1. What is the linear regression equation (rounded to tenths)? y = 4.8x + 9.2 2. What is the slope and what does it mean in context? The slope is 4.8. It means that the salary goes up 4.8 thousand dollars each year. In other words, the salary increases $4800 per year. 3. What is the y-intercept and what does it mean in context? The y-intercept is 9.2. It means that the starting salary was 9.2 thousand dollars. In other words, the starting salary was $9200. 4. What is the correlation coefficient (rounded to nearest hundredth)? The correlation coefficient is 0.98. 5. What does the correlation coefficient tell us about this data? The correlation coefficient tells us that this data has a very strong positive correlation. 6. What is the predicted salary for someone with 10 years experience? 7. It that an example of interpolation or extrapolation? Why?

  9. Warm Up - Linear Regression Models Name: Date: Period: Use the Desmos Graphing Calculator to answer the following. 1. What is the linear regression equation (rounded to tenths)? y = 4.8x + 9.2 2. What is the slope and what does it mean in context? The slope is 4.8. It means that the salary goes up 4.8 thousand dollars each year. In other words, the salary increases $4,800 per year. 3. What is the y-intercept and what does it mean in context? The y-intercept is 9.2. It means that the starting salary was 9.2 thousand dollars. In other words, the starting salary was $9,200. 4. What is the correlation coefficient (rounded to nearest hundredth)? The correlation coefficient is 0.98. 5. What does the correlation coefficient tell us about this data? The correlation coefficient tells us that this data has a very strong positive correlation. 6. What is the predicted salary for someone with 10 years experience? Someone with ten years of experience should make $57,200. 7. It that an example of interpolation or extrapolation? Why? y = 4.8x + 9.2 y = 4.8(10) + 9.2 y = 48 + 9.2 y = 57.2

  10. Warm Up - Linear Regression Models Name: Date: Period: Use the Desmos Graphing Calculator to answer the following. 1. What is the linear regression equation (rounded to tenths)? y = 4.8x + 9.2 2. What is the slope and what does it mean in context? The slope is 4.8. It means that the salary goes up 4.8 thousand dollars each year. In other words, the salary increases $4,800 per year. 3. What is the y-intercept and what does it mean in context? The y-intercept is 9.2. It means that the starting salary was 9.2 thousand dollars. In other words, the starting salary was $9,200. 4. What is the correlation coefficient (rounded to nearest hundredth)? The correlation coefficient is 0.98. 5. What does the correlation coefficient tell us about this data? The correlation coefficient tells us that this data has a very strong positive correlation. 6. What is the predicted salary for someone with 10 years experience? Someone with ten years of experience should make $57,200. 7. It that an example of interpolation or extrapolation? Why? This is an example of interpolation because 10 years experience falls between the lowest and highest values of the years of experience. y = 4.8x + 9.2 y = 4.8(10) + 9.2 y = 48 + 9.2 y = 57.2

  11. Warm Up - Linear Regression Models Name: Date: Period: Use the Desmos Graphing Calculator to answer the following.

  12. I can: • calculate a linear regression equation • determine the correlation coefficient • interpret slope and y-intercept • use the regression equation to predict • calculate the residual at a given point Scatter Plots and Lines of Best Fit

  13. Copy the table into your spiral. Practice: Player Height vs. Average Basketball Points Scored Use the linear regression equation to predict the points scored by a player that is 64 inches tall. Interpolation or Extrapolation? Use the linear regression equation to predict the height of a player who scores 16 points. Interpolation or Extrapolation?

  14. y = 0.18x + 1.87 r = 0.3215 Here is the regression equation and correlation coefficient for this data. What do we know from these items? Practice: Player Height vs. Average Basketball Points Scored Use the linear regression equation to predict the points scored by a player that is 64 inches tall. Interpolation or Extrapolation? Use the linear regression equation to predict the height of a player who scores 16 points. Interpolation or Extrapolation?

  15. y = 0.18x + 1.87 r = 0.3215 This is a weak positive correlation. We can make predictions, but they are not very reliable. Practice: Player Height vs. Average Basketball Points Scored Use the linear regression equation to predict the points scored by a player that is 64 inches tall. Interpolation or Extrapolation? Use the linear regression equation to predict the height of a player who scores 16 points. Interpolation or Extrapolation?

  16. y = 0.18x + 1.87 Use the linear regression equation to predict the points scored by a player that is 64 inches tall. Interpolation or Extrapolation? Practice: Player Height vs. Average Basketball Points Scored

  17. y = 0.18x + 1.87 Use the linear regression equation to predict the points scored by a player that is 64 inches tall. Interpolation or Extrapolation? y = 0.18(64) + 1.87 Practice: Player Height vs. Average Basketball Points Scored

  18. y = 0.18x + 1.87 Use the linear regression equation to predict the points scored by a player that is 64 inches tall. Interpolation or Extrapolation? y = 0.18(64) + 1.87 y = 11.52 + 1.87 Practice: Player Height vs. Average Basketball Points Scored

  19. y = 0.18x + 1.87 Use the linear regression equation to predict the points scored by a player that is 64 inches tall. Interpolation or Extrapolation? y = 0.18(64) + 1.87 y = 11.52 + 1.87 y = 13.39 Practice: Player Height vs. Average Basketball Points Scored

  20. y = 0.18x + 1.87 Use the linear regression equation to predict the points scored by a player that is 64 inches tall. Interpolation or Extrapolation? y = 0.18(64) + 1.87 y = 11.52 + 1.87 y = 13.39 Someone 64 inches tall should score an average of 13.39 points. Practice: Player Height vs. Average Basketball Points Scored

  21. y = 0.18x + 1.87 Use the linear regression equation to predict the points scored by a player that is 64 inches tall. Interpolation or Extrapolation? y = 0.18(64) + 1.87 y = 11.52 + 1.87 y = 13.39 Someone 64 inches tall should score an average of 13.39 points. This is an extrapolation because 64 inches is outside of the data. Practice: Player Height vs. Average Basketball Points Scored

  22. y = 0.18x + 1.87 Use the linear regression equation to predict the height of a player who scores 16 points. Interpolation or Extrapolation? Practice: Player Height vs. Average Basketball Points Scored

  23. y = 0.18x + 1.87 Use the linear regression equation to predict the height of a player who scores 16 points. Interpolation or Extrapolation? 16 = 0.18x + 1.87 Practice: Player Height vs. Average Basketball Points Scored

  24. y = 0.18x + 1.87 Use the linear regression equation to predict the height of a player who scores 16 points. Interpolation or Extrapolation? 16 = 0.18x + 1.87 14.13 = 0.18x Practice: Player Height vs. Average Basketball Points Scored

  25. y = 0.18x + 1.87 Use the linear regression equation to predict the height of a player who scores 16 points. Interpolation or Extrapolation? 16 = 0.18x + 1.87 14.13 = 0.18x 78.5 = x Practice: Player Height vs. Average Basketball Points Scored

  26. y = 0.18x + 1.87 Use the linear regression equation to predict the height of a player who scores 16 points. Interpolation or Extrapolation? 16 = 0.18x + 1.87 14.13 = 0.18x 78.5 = x A player that scores 16 points should be 78.5 inches tall. Practice: Player Height vs. Average Basketball Points Scored

  27. y = 0.18x + 1.87 Use the linear regression equation to predict the height of a player who scores 16 points. Interpolation or Extrapolation? 16 = 0.18x + 1.87 14.13 = 0.18x 78.5 = x A player that scores 16 points should be 78.5 inches tall. This is an interpolation because 16 points is inside the data. Practice: Player Height vs. Average Basketball Points Scored

  28. Scatter Plots and Lines of Best Fit Day 3 - Residuals

  29. I can: • calculate the residual at a data point Residuals

  30. I can: • calculate the residual at a data point • interpret the residual for the situation Residuals

  31. Residuals • the difference between the actual value and the predicted value from the regression line • allows us to determine if the actual value is above or below the prediction line and by how much (actual - predicted) • when looking at data, residuals may help in drawing conclusions and making comparisons

  32. Residuals • the difference between the actual value and the predicted value from the regression line • allows us to determine if the actual value is above or below the prediction line and by how much (actual - predicted) • when looking at data, residuals may help in drawing conclusions and making comparisons

  33. Residuals • the difference between the actual value and the predicted value from the regression line • allows us to determine if the actual value is above or below the prediction line and by how much (actual - predicted) • when looking at data, residuals may help in drawing conclusions and making comparisons

  34. Residuals • the difference between the actual value and the predicted value from the regression line • allows us to determine if the actual value is above or below the prediction line and by how much (actual - predicted) • when looking at data, residuals may help in drawing conclusions and making comparisons

  35. Use the interactive graph to explore residuals. Let’s examine some residuals from our basketball example. y = 0.18x + 1.87 Teachers: Click here to access the applet. Scroll down to find the graph. Residuals

  36. Let’s examine some residuals from our basketball example. y = 0.18x + 1.87 Residuals

  37. Let’s examine some residuals from our basketball example. y = 0.18x + 1.87 Residuals

  38. Let’s examine some residuals from our basketball example. Desmos can calculate the residuals for us. y = 0.18x + 1.87 Residuals

  39. Let’s examine some residuals from our basketball example. y = 0.18x + 1.87 Residuals

  40. Let’s examine some residuals from our basketball example. The data point when the height was 77 inches has a positive residual. That means that the prediction line UNDERESTIMATES the actual data at this point. y = 0.18x + 1.87 Residuals

  41. Let’s examine some residuals from our basketball example. These data points have a negative residual. That means that the prediction line OVERESTIMATES the actual data at these points. y = 0.18x + 1.87 Residuals

  42. How do we calculate the residual without Desmos? Let’s examine some residuals from our basketball example. y = 0.18x + 1.87 Residuals

  43. How do we calculate the residual without Desmos? Let’s examine some residuals from our basketball example. Note the actual data point: y = 0.18x + 1.87 Residuals

  44. How do we calculate the residual without Desmos? Let’s examine some residuals from our basketball example. Note the actual data point: (77, 19) y = 0.18x + 1.87 Residuals

  45. How do we calculate the residual without Desmos? Let’s examine some residuals from our basketball example. Note the actual data point: (77, 19) Use the equation to find the predicted value: y = 0.18x + 1.87 Residuals

  46. How do we calculate the residual without Desmos? Let’s examine some residuals from our basketball example. Note the actual data point: (77, 19) Use the equation to find the predicted value: y = 0.18x + 1.87 y = 0.18x + 1.87 Residuals

  47. How do we calculate the residual without Desmos? Let’s examine some residuals from our basketball example. Note the actual data point: (77, 19) Use the equation to find the predicted value: y = 0.18(77) + 1.87 y = 13.86 + 1.87 y = 15.73 y = 0.18x + 1.87 y = 0.18x + 1.87 Residuals

  48. How do we calculate the residual without Desmos? Let’s examine some residuals from our basketball example. Note the actual data point: (77, 19) Use the equation to find the predicted value: y = 0.18(77) + 1.87 y = 13.86 + 1.87 y = 15.73 Subtract ACTUAL minus PREDICTED: y = 0.18x + 1.87 y = 0.18x + 1.87 Residuals

  49. How do we calculate the residual without Desmos? Let’s examine some residuals from our basketball example. Note the actual data point: (77, 19) Use the equation to find the predicted value: y = 0.18(77) + 1.87 y = 13.86 + 1.87 y = 15.73 Subtract ACTUAL minus PREDICTED: 19 - 15.73 = 3.27 y = 0.18x + 1.87 y = 0.18x + 1.87 Residuals

  50. How do we calculate the residual without Desmos? Let’s examine some residuals from our basketball example. Note the actual data point: (77, 19) Use the equation to find the predicted value: y = 0.18(77) + 1.87 y = 13.86 + 1.87 y = 15.73 Subtract ACTUAL minus PREDICTED: 19 - 15.73 = 3.27 y = 0.18x + 1.87 y = 0.18x + 1.87 Residuals

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