Moodle Auto Accidents Tickets

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In 2001, Progressive Insurance       Miles from    % of Accidents
  asked customers who had been       home
  involved in auto accidents how
  far they were from home when       Less than 1   23
  the accident happened. The         1 to 5        29
  data are summarized in the
  table.                             6 to 10       17
  a)   Create an appropriate         11 to 15      8
       graph of these data
                                     16 to 20      6
  b)   Do these data indicate that
       driving near home is          Over 20       17
       particularly dangerous?
                       Review questions

 When describing a scatterplot, what four things should
 you always mention?
    Direction, form, strength, unusual features (such as outliers,
 What does correlation measure?
    Measures the strength of the linear association between two
     quantitative variables
 Explain the difference between association and
    Association is a vague term describing the relationship between two
     variables. Correlation is a precise term describing the strength and
     direction of the linear relationship between quantitative variables
                     Review questions

 What three conditions are necessary in order to use
 correlation as a measure of association?
    Quantitative Variables condition
    Straight Enough condition
    Outlier Condition
                    Review questions

 What does a correlation near zero indicate?
   There is almost no linear association between the variables

 Sketch an example of a scatterplot that shows two
  variables with a strong association but a weak
 Is correlation resistant or nonresistant to outliers?
                    Review questions

 A school board study found a moderately strong
 negative association between the number of hours
 high school seniors worked at part-time jobs after
 school hours and the students’ grade point averages.
 Explain in this context what “negative association”
    Students who worked more hours tended to have lower grades
        Correlation…more to think about…

 Hoping to improve student performance, the school
 board passed a resolution urging parents to limit the
 number of hours students be allowed to work. Do
 you agree or disagree with the school board’s
 reasoning? Explain.
    They are mistakenly attributing the association to cause and
     effect. “Association does not imply causation.” Maybe
     students with low grades are more likely to seek jobs, or maybe
     there is some other factor in their home life that leads both to
     lower grades and to the desire or need to work. (a lurking
Demo: Effect of individual points on correlation

 Points near the center of the scatterplot have little
 Points that fit the pattern increase the strength (and
  more so the farther the point is from the center)
 Points that don’t fit the pattern decrease (and can
  even reverse the sign of ) the correlation
         Re-expressing data to make it linear

 The variables year and U.S.         Year   Population
  population, in millions of people          (millions)
  are displayed. The association
  between year and population is      1800   5
  strong, positive, and curved.       1850   23
  Population has been increasing
  over the last 200 years.            1900   76
  Furthermore, the rate of            1950   151
  population growth has been
                                      2000   285
  increasing. The U.S. population
  has been growing faster in more
  recent years. We will attempt to
  straighten the scatter plot using
  a logarithmic re-expression and
  a square root re-expression.
     Re-expressing data to make it linear

Ex 1. Gordon Moore, one of the founders of Intel
 Corporation, predicted in 1965 that the number of
 transistors on an integrated circuit chip would
 double every 18 months. This is “Moore’s Law,” one
 way to measure the revolution in computing. Here
 are the data on the dates and number of transistor
 for Intel microprocessors.
Processor     Date          Transistors
4004                 1971                    2,250
8008                 1972                    2,500
8080                 1974                    5,000
8086                 1978                   29,000
286                  1982                  120,000
386                  1985                  275,000
486 DX               1989                 1,180,000
Pentium              1993                 3,100,000
Pentium II           1997                 7,500,000
Pentium III          1997            24,000,000
Pentium 4            2000            42,000,000

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