Regression to Mediocrity

1
Regression to Mediocrity

• Galton and the origins of Regression

2
Midterm scores

• MT2 10 .9MT1 random noise
• Mean on MT1 was 75. Whats mean on MT2?
• Compute your score on MT2.

3
Why?

• Regression line is skill, genetics luck
• The skill persists, but the luck is random and,
  on average, 0.
• Skill good luck on MT 1 ---gt Skill 0 luck on
  MT 2, on average

4
Sir Francis Galton
5
Inheritance

• How is talent passed on genetically? Is it?
• Talent hard to measure, so instead examine height.

6
Data

• library(UsingR)
• data(galton)
• attach(galton)
• Plot, then predict childs height from parents.
• What are mean heights of each group?

7
Galton's Graph
8

• If youre above average height, what height
  should you predict your child to be?
• Is this height above or below average?
• If youre below average in height, what height
  should you predict your child to be?
• Is this above or below average

9
Regression Fallacy

• So are children getting closer to average?
• No. The average height is in fact increasing.
  Variation about the average is about the same in
  both generations.
• What about the father of a very tall person? Is
  he also likely to be closer to the mean?
• A "statistical artifact"

10
Horace Secrist

• The Triumph of Mediocrity in Business
• Profitably companies become less profitable
• poorly performing companies do better.

11
From wikipedia

• The calculation and interpretation of
  "improvement scores" on standardized educational
  tests in Massachusetts probably provides another
  example of the regression fallacy. In 1999,
  schools were given improvement goals. For each
  school, the Department of Education tabulated the
  difference in the average score achieved by
  students in 1999 and in 2000. It was quickly
  noted that most of the worst-performing schools
  had met their goals, which the Department of
  Education took as confirmation of the soundness
  of their policies. However, it was also noted
  that many of the supposedly best schools in the
  Commonwealth, such as Brookline High School (with
  18 National Merit Scholarship finalists) were
  declared to have failed. As in many cases
  involving statistics and public policy, the issue
  is debated, but "improvement scores" were not
  announced in subsequent years and the findings
  appear to be a case of regression to the mean.

12
(No Transcript)
13
Cover Jinx

• St. Louis Ram's quarterback Kurt Warner refused
  to appear, so cat appeared alone.
• 2456 people on covers 913 (37.2) were "jinxed"