Stat 217

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Stat 217 Lecture 15

• Relationships (Ch. 2, 9,11)

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Announcements

• My 3-4 office hours today cancelled but will be
  in my office 1-3 and 4-5
• Project presentations Wed and Thurs pm
• peer review forms
• Final Exam (Monday 1010-100)
• Can you come at 9?
• Can you stay until 2?
• Review in class Wednesday bring Qs!
• Review Session Sunday?

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Last Time Comparing Several Populations

• Proportions
• Segmented bar graph
• H0 p1 pI
• Ha at least one p differs
• Chi-square test
• two-way table
• TC expected cell counts gt 5, random samples or
  randomization
• Follow-up analysis

• Means
• Stacked boxplot
• H0 m1 mI
• Ha at least one m differs
• ANOVA
• TC random samples or randomization
• normal population or ns large
• equal variance (SD ratio lt2)

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Example 15-1 (p. 138)

• Do underclassmen choose different lifetime
  achievements?
• one sample Stat 217 students
• underclassmen upperclassmen
• nobel 14 17
• academy 6 9
• olympic 16 12

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New situation

• One sample, classified according to 2 variables
• variable 1 classrank (categorical)
• variable 2 achievement (categorical)
• Describing the data
• Making inferences about all Stat 217 students

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Example 15-2
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Example 15-2

• Graphical summary scatterplot

300 0
Atlanta (576, 178)
178
airfare
response
Boston (370, 138)
576
0 1500
explanatory variable
distance
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Example 15-2
each dot represents one city
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Example 15-2

• To describe scatterplot
• 1) Direction
• positive association
• negative association

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Example 15-2

• To describe scatterplot
• 1) Direction
• positive association
• negative association

• 2) Strength
• how strongly do they follow the pattern
• 3) Linear?
• do the points fall in a line

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Example 15-2
each dot represents one city
fairly strong, positive, linear association
St. Louis
Chicago
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Example 15-3

• Strongly positive B ¼ mile vs. acc0-60
• Almost strongly positiveF hwy mpg vs. city mpg
• Mildly positive I ¼ mile vs. city mpg
• Slightly positive E front weight vs. city mpg
• Virtually none C fuel capacity vs. page number
• Slightly negativeH front weight vs. fuel
  capacity
• Mildly negative A ¼ mile vs. weight
• Almost strongly negativeG hwy mpg vs. fuel cap
• Strongly negative D city mpg vs. weight

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Example
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Extrapolation
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Summary

• Graphical summary scatterplot
• Numerical summary correlation coefficient (if
  linear)
• Model least squares regression line
• residual observation fitted value
• prediction (using x near those used to find
  equation)
• interpreting regression coefficients

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Summary

• If relationship appears linear, fit regression
  model
• Examine residual plots
• If technical conditions are met, test H0 b0
  vs. Ha blt gt ?0
• t-statistic with dfn-2
• If p-value small, have evidence of a
  statistically significant relationship between
  variable 1 and variable 2