1 / 210

Last Time

Last Time. T Distribution Confidence Intervals Hypothesis tests Relationships Between Variables Scatterplots (visualization) Aspects of Relations Form Direction Strength. Reading In Textbook. Approximate Reading for Today’s Material: Pages 101-105 , 447-465, 511-516

hollis
Télécharger la présentation

Last Time

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Last Time • T Distribution • Confidence Intervals • Hypothesis tests • Relationships Between Variables • Scatterplots (visualization) • Aspects of Relations • Form • Direction • Strength

  2. Reading In Textbook Approximate Reading for Today’s Material: Pages 101-105 , 447-465, 511-516 Approximate Reading for Next Class: Pages 110-135, 560-574

  3. Scatterplot E.g. Class Example 16: How does HW score predict Final Exam? xi = HW, yi = Final Exam • In top half of HW scores: Better HW  Better Final

  4. Important Aspects of Relations • Form of Relationship • Direction of Relationship • Strength of Relationship

  5. I. Form of Relationship • Linear: Data approximately follow a line Previous Class Scores Example http://www.stat-or.unc.edu/webspace/courses/marron/UNCstor155-2009/ClassNotes/Stor155Eg16.xls Final vs. High values of HW is “best” • Nonlinear: Data follows different pattern Nice Example: Bralower’s Fossil Data http://www.stat-or.unc.edu/webspace/courses/marron/UNCstor155-2009/ClassNotes/Stor155Eg17.xls

  6. Bralower’s Fossil Data http://www.stat-or.unc.edu/webspace/courses/marron/UNCstor155-2009/ClassNotes/Stor155Eg17.xls From T. Bralower, formerly of Geological Sci. Studies Global Climate, millions of years ago

  7. II. Direction of Relationship • Positive Association X bigger  Y bigger • Negative Association X bigger  Y smaller Note: Concept doesn’t always apply: Bralower’s Fossil Data

  8. III. Strength of Relationship Idea: How close are points to lying on a line? Revisit Class Scores Example: http://www.stat-or.unc.edu/webspace/courses/marron/UNCstor155-2009/ClassNotes/Stor155Eg16.xls

  9. Comparing Scatterplots Additional Useful Visual Tool

  10. Comparing Scatterplots Additional Useful Visual Tool: • Overlaying multiple data sets

  11. Comparing Scatterplots Additional Useful Visual Tool: • Overlaying multiple data sets • Allows comparison

  12. Comparing Scatterplots Additional Useful Visual Tool: • Overlaying multiple data sets • Allows comparison • Use different colors or symbols

  13. Comparing Scatterplots Additional Useful Visual Tool: • Overlaying multiple data sets • Allows comparison • Use different colors or symbols • Easy in EXCEL (colors are automatic)

  14. Comparing Scatterplots HW HW: 2.21, 2.25

  15. III. Strength of Relationship Idea: How close are points to lying on a line? Revisit Class Scores Example: http://www.stat-or.unc.edu/webspace/courses/marron/UNCstor155-2009/ClassNotes/Stor155Eg16.xls

  16. III. Strength of Relationship Idea: How close are points to lying on a line? Now get quantitative

  17. Section 2.2: Correlation Main Idea: Quantify Strength of Relationship

  18. Section 2.2: Correlation Main Idea: Quantify Strength of Relationship Context: • A numerical summary

  19. Section 2.2: Correlation Main Idea: Quantify Strength of Relationship Context: • A numerical summary • In spirit of mean and standard deviation

  20. Section 2.2: Correlation Main Idea: Quantify Strength of Relationship Context: • A numerical summary • In spirit of mean and standard deviation • But now applies to pairs of variables

  21. Section 2.2: Correlation Main Idea: Quantify Strength of Relationship Specific Goals

  22. Section 2.2: Correlation Main Idea: Quantify Strength of Relationship Specific Goals: • Near 1: for positive relat’ship & nearly linear

  23. Section 2.2: Correlation Main Idea: Quantify Strength of Relationship Specific Goals: • Near 1: for positive relat’ship & nearly linear • > 0: for positive relationship (slopes up)

  24. Section 2.2: Correlation Main Idea: Quantify Strength of Relationship Specific Goals: • Near 1: for positive relat’ship & nearly linear • > 0: for positive relationship (slopes up) • = 0: for no relationship

  25. Section 2.2: Correlation Main Idea: Quantify Strength of Relationship Specific Goals: • Near 1: for positive relat’ship & nearly linear • > 0: for positive relationship (slopes up) • = 0: for no relationship • < 0: for negative relationship (slopes down)

  26. Section 2.2: Correlation Main Idea: Quantify Strength of Relationship Specific Goals: • Near 1: for positive relat’ship & nearly linear • > 0: for positive relationship (slopes up) • = 0: for no relationship • < 0: for negative relationship (slopes down) • Near -1: for negative relat’ship & nearly linear

  27. Correlation - Approach Numerical Approach

  28. Correlation - Approach Numerical Approach: for symmetric around

  29. Correlation - Approach Numerical Approach: for symmetric around has similar properties

  30. Correlation - Approach Numerical Approach: for symmetric around has similar properties Worked out Example : http://www.stat-or.unc.edu/webspace/courses/marron/UNCstor155-2009/ClassNotes/Stor155Eg18-new.xls

  31. Correlation – Graphical View Plots (a) & (b): illustrating : • > 0 for positive relationship

  32. Correlation – Graphical View Plots (a) & (b): illustrating : • > 0 for positive relationship

  33. Correlation – Graphical View Plots (a) & (b): illustrating : • > 0 for positive relationship • < 0 for negative relationship

  34. Correlation – Graphical View Plots (a) & (b): illustrating : • > 0 for positive relationship • < 0 for negative relationship

  35. Correlation – Graphical View Plots (a) & (b): illustrating : • Bigger for data closer to line

  36. Correlation – Graphical View Plots (a) & (b): illustrating : • Bigger for data closer to line

  37. Correlation – Graphical View But not all goals are satisfied

  38. Correlation – Graphical View Problem 1: Not between -1 & 1

  39. Correlation – Graphical View Problem 2: Feels “Scale”, see plot (c) (just 10  1 vertical rescaling of)

  40. Correlation – Graphical View Problem 2: Feels “Scale”, see plot (c) (just 10  1 vertical rescaling of) ( feels factor of 1/10)

  41. Correlation – Graphical View Problem 3: Feels “Shift” even more, see (d) (even gets sign wrong!)

  42. Correlation – Graphical View Problem 3: Feels “Shift” even more, see (d) (even gets sign wrong!) • Data trend upwards

  43. Correlation – Graphical View Problem 3: Feels “Shift” even more, see (d) (even gets sign wrong!) • Data trend upwards • But < 0

  44. Correlation - Approach Solution to above problems

  45. Correlation - Approach Solution to above problems: Standardize!

  46. Correlation - Approach Solution to above problems: Standardize! Define Correlation

  47. Correlation - Approach Solution to above problems: Standardize! Define Correlation

  48. Correlation - Example Revisit above example http://www.stat-or.unc.edu/webspace/courses/marron/UNCstor155-2009/ClassNotes/Stor155Eg18-new.xls • r is always same, and ~1, for (a)

  49. Correlation - Example Revisit above example http://www.stat-or.unc.edu/webspace/courses/marron/UNCstor155-2009/ClassNotes/Stor155Eg18-new.xls • r is always same, and ~1, for (a), (c)

  50. Correlation - Example Revisit above example http://www.stat-or.unc.edu/webspace/courses/marron/UNCstor155-2009/ClassNotes/Stor155Eg18-new.xls • r is always same, and ~1, for (a), (c), (d)

More Related