Linear Regression Examples

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Linear Regression Examples

• Lecture Notes
• Febrauary 2, 2002
• R. Sinn

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Clicker Question 1

• Which of the following terms is NOT a synonym of
  the others?
• Line of Best Fit
• Regression Line
• Nickelback
• Prediction Equation
• Least Squares Line

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Clicker Question 2

• Linear regression can compare
• Two categorical variables
• Two numeric variables
• A numeric variable and a categorical variable
  that is hierarchical
• B C only
• None of the above

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Clicker Question 3

• The statistic r is called
• Correlation coefficient
• Coefficient of determination
• Slope

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Clicker Question 4

• Biochemical oxygen demand (BOD) measures organic
  pollutants in water. BOD is hard to measure
  accurately. Total organic carbon (TOC) is easy to
  measure, so it is common to measure TOC and use
  regression to predict BOD. (Both BOD and TOC are
  measured in milligrams per liter of water.) A
  typical regression equation for water entering a
  municipal treatment plant is
• Given the equation above, predict TOC when BOD
  152.5 mg/l
• 137.98 mg/l
• 148.17 mg/l
• 162.34 mg/l
• 174.39 mg/l

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Clicker Question 5

• A typical regression equation for water entering
  a municipal treatment plant is
• Given this equation, predict BOD when TOC 99.2
  mg/l
• 102.6 mg/l
• 94.1 mg/l
• 99.2 mg/l
• 93.9 mg/l

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Clicker Question 6

• Which of the following statements is true?
• A decrease in pirates has caused global warming
• The Baptist church drives people to drink
• Drink drives people to the Baptist Church
• Correlation does not imply causation

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Linear Regression Analysis

• Scatter Plot Check
• Linear Relationship?
• Run Regression
• Analyze r
• Line of Best Fit
• Analyze R2
• Prediction
• Analyze slope of line of best fit

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Example 1

• The table below compares the average number of
  employees in a group health insurance program (x)
  to the average administrative cost as a
  percentage of claims (y)

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Example 2

• Pediatrics a childs weight (kg) can predict the
  metabolic rate (100 kcal/24 hr).

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Prediction

• Example 1
• Predict the administrative costs for a plan
  purchased by a company employing 10 workers.
• Example 2
• Predict the metabolic rate of a 10 kg child.

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Backwards Prediction

• Example 1
• A certain firm has administrative costs of 25.
  How many workers do they employ?
• Example 2
• If the metabolic rate of a child is 550 kcal/24
  hr, how much does the likely weigh?

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Slopes of Lines of Best Fit

• What does the slope mean in terms of the
  relationship between x and y in a regression?

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Answers 1

• Example 1
• r -.92
• y -.28 x 36.8
• R2 .855
• Strong, negative relationship
• Number of employees accounts for 86 of the
  variance in administrative costs.

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Answers 2

• Prediction with Example 1
• y -.28 x 36.8
• If x 10, then y 33.98
• If y 25, then x 41.84
• Analysis of Slope in Example 1
• For every employee added, percentage
  administrative costs for that businesss heath
  plan decreases by .28.

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Ann Coulter Example

• Who is Ann?
• Website Link
• Who is Brian Nichols?
• Ann wrote a scathing article about women on
  police forces after the Brian Nichols incident
  called Freeze! I Just Had My Nails Done!

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Ann Coulter Example

• Unable to use intermediate force, like a bop on
  the nose, female officers quickly go to fatal
  force. According to Lotts analysis, each 1
  increases in the number of white female officers
  in a police force increases the number of
  shooting of civilians by 2.7
• Adding males a police force decreases the number
  of civilians accidentally shot by police. Adding
  black males decreases civilian shootings by
  police even more.
• Lott says, Increasing the number of female
  officers by 1 percentage point appears to
  increase the number of assaults on police by 15
  to 19.

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Clicker Question 7

• Quote Adding males a police force decreases the
  number of civilians accidentally shot by police.
  Adding black males decreases civilian shootings
  by police even more.
• The study Ann is quoting was a regression study.
  The findings we infer are
• Additional (black) males are positively
  correlated to number of civilians shot
  accidentally by police
• Additional (black) males are negatively
  correlated to number of civilians shot
  accidentally by police
• No meaningful relationship exists.

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Clicker Question 8

• Quote Lott says, Increasing the number of
  female officers by 1 percentage point appears to
  increase the number of assaults on police by 15
  to 19.
• Question What regression parameter is being
  analyzed?
• The correlation coefficient
• The coefficient of determination
• The slope of the regression line
• The intercept of the regression line
• None of the above

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Clicker Question 9

• Quote Unable to use intermediate force, like a
  bop on the nose, female officers quickly go to
  fatal force. According to Lotts analysis, each
  1 increases in the number of white female
  officers in a police force increases the number
  of shooting of civilians by 2.7
• Question In terms of statistics (not my
  political opinions), Ann has very strong
  argument.
• I strongly agree
• I agree somewhat
• I disagree somewhat
• I disagree strongly