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B ivariate Distributions

B ivariate Distributions. Overview. I. Exploring Data. Describing patterns and departures from patterns (20%-30%)

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B ivariate Distributions

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  1. Bivariate Distributions Overview

  2. I. Exploring Data Describing patterns and departures from patterns (20%-30%) Exploring analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis should be placed on interpreting information from graphical and numerical displays and summaries.

  3. I. Exploring Data

  4. I. Exploring Data What should you discuss when describing a bivariate relationship?

  5. I. Exploring Data What should you discuss when describing a bivariate relationship? 1. Describe the cases and variables.

  6. I. Exploring Data What should you discuss when describing a bivariate relationship? Describe the cases and variables. Describe the shape (linear or curved).

  7. I. Exploring Data What should you discuss when describing a bivariate relationship? Describe the cases and variables. Describe the shape (linear or curved). Describe the trend (positive or negative, in context).

  8. I. Exploring Data What should you discuss when describing a bivariate relationship? Describe the cases and variables. Describe the shape (linear or curved). Describe the trend (positive or negative, in context – Least squares line). Describe the strength (moderate, weak, strong – r and r2). Does the relationship generalize? (to other cases, other times) Suggest possible reasons for the relationship.

  9. What is r? r is Pearson’s correlation coefficient. It is a measure of strength of linear association. Once we’ve determined from a graph that the relationship is linear, we can use r to describe the strength of the relationship.

  10. What is r?

  11. What is r? r is calculated by converting the x and y coordinates to z-scores, then finding the product for each point. The average (almost) product of the z-scores for each point is r.

  12. What is r2? This is a plot of the number of calories per 5 oz. serving of pizza and the number of grams of fat per serving.

  13. What is r2? Our best estimate for the typical number of calories in a serving of pizza would be to use the mean number of calories.

  14. What is r2? Of course there is error in this estimate. When we calculate the typical error (standard deviation) we square the amount of error.

  15. What is r2? The total amount of squared error is called the Total Sum of Squares (SST).

  16. What is r2? But if we use information about the amount of fat, we can create a regression line to minimize this squared error.

  17. What is r2? The sum of the squared error from the regression line is called the Sum of Squared Error (SSE).

  18. What is r2? Notice the amount of squared error reduced substantially. It dropped from 24490 to 4307. We can calculate the amount of error that was ‘explained’ by the regression line. This is r2. 82% of the variation in calories can be explained by using the regression equation with fat as a predictor.

  19. Multiple Choice Questions • Read and think for one minute, and write your answer. • Discuss with group members for 30 seconds and decide on a final answer. • Discuss as a group for as long as we need to. . .

  20. Source: AP Practice Exam

  21. Source: AP Practice Exam

  22. Answer: A

  23. Source: 1997 AP Exam

  24. Answer: B

  25. Source: AP Practice Exam

  26. Answer: A

  27. Source: 1997 AP Exam

  28. Answer: A

  29. Answer: A

  30. Source: AP Practice Exam

  31. Source: AP Practice Exam

  32. Source: AP Practice Exam

  33. Source: AP Practice Exam

  34. Source: 1997 AP Exam

  35. Source: 1997 AP Exam

  36. Source: 1997 AP Exam

  37. Source: 1997 AP Exam

  38. Source: 1997 AP Exam

  39. Source: 1997 AP Exam

  40. Source: 1997 AP Exam

  41. Source: 2011 AP Exam

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