Economics 173 Business Statistics

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Economics 173Business Statistics

• Lecture 11
• Fall, 2001
• Professor J. Petry
• http//www.cba.uiuc.edu/jpetry/Econ_173_fa01/

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Linear Regression Review

• Exam is Thursday, October 4th, 7-9 in Lincoln
  Theatre. There is no class Thursday. Office hours
  will be extended prior to the exam.
• Petry office hours Tues 2-4, Wed 1130-1230
• TAs will post hours on web-board.
• Well get as far as possible through two topics
  of importance for Thursdays exam
• Simple Linear Regression
• Identifying the proper technique

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To calculate the estimates of the
coefficients that minimize the differences
between the data points and the line, use the
formulas
The regression equation that estimates the
equation of the first order linear model is
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Example Armanis Pizza

• Armanis Pizza is considering locating at the U
  of I campus. To do their financial analysis, they
  first need to estimate sales for their product.
• They have data from their existing 10 locations
  on other college campuses.
• Estimate sales for the University of Illinois,
  with a college population of 35,000.

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Example Armanis Pizza

• Begin by plotting the data

• Followed by calculating the statistics of your
  regression

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Example Armanis Pizza

• Solve for b1, then b0 using the second formula

• After obtaining values for your regression line,
  interpret its meaning.
• Finally, plug in the value for your independent
  variable (35, not 35,000) into the formula, and
  predict sales!

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Example Armanis Pizza Excel Output
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17.4 Error Variable Required Conditions

• The error e is a critical part of the regression
  model.
• Four requirements involving the distribution of e
  must be satisfied.
• The probability distribution of e is normal.
• The mean of e is zero E(e) 0.
• The standard deviation of e is se for all values
  of x.
• The set of errors associated with different
  values of y are all independent.

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Simple Linear Regression-Ex 2

• A dog trainer has noticed that his dog Chip seems
  to perform better in dog shows if he has been
  given speedy biscuitsthe biscuit with a zip!
  prior to the show. To examine this possible
  relationship, he records the number of biscuits
  Chip consumed prior to each show, and the score
  (1-10, with 10 being the highest) from each show.
  
• Find b0
• Find b1
• Interpret the slope coefficient.

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Linear RegressionDog Show Ex.
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Identifying the correct Technique

• Describe a single population
• Using the same data, you could use all the single
  population tests we have discussed, depending
  upon what information you have, and what you are
  after. In this case, you have the alphabetical
  listing of race times from last years race to
  work from.
• Your roommate thinks the average time to complete
  the Chicago Marathon gt4 hours?
• Your roommate thinks the percentage of racers
  finishing the race under 3 hours is less than 5.
  
• Your roommate is also a male chauvenist pig, and
  believes that male runners are superior. This is
  demonstrated by the fact that their race times
  are more spread out than womens. All women are
  mediocre, and hence are clumped in the middle of
  the pack, while some men are at the front of the
  packthey have achieved their superior status
  while many are also at the backthey are on their
  way to realizing their superior status.

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Identifying the correct Technique

• Compare two populations
• He is from the Chicago area, and naturally knows
  that all people from the Chicago area are also
  superior. This can be easily verified by
  categorizing his sample by race time, and
  demonstrating that Chicagoans have a better race
  time than non-Chicagoans.
• To do further analysis, he obtains the results
  from two years ago as well. Part of being
  superior is being consistent, he therefore plans
  to use this data to show that Chicagoans race
  times are more consistent in their race times
  than are non-Chicagoans.
• A critical component to being a male chauvenist
  pig, is eating like one. He eats pigs feet for
  breakfast and believes this is one of his keys to
  success. He wants to verify that eating pigs feet
  improves performance, so he obtains data from
  each year those that eat pigs feet and those
  that dont and compares scores.
• He does the same thing, but this time he takes
  those that have seen the light since the race
  two years ago, and began eating pigs feet before
  the last race, but hadnt yet started before the
  race two years ago.

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Identifying the correct Technique

• Compare two populations
• Unfortunately, he believes the Chicago Marathon
  is going down hill. To test this claim, all he
  believes he has to do is show that the number of
  male Chicagoans running the race is less as a
  percentage of total racers than it was two years
  ago.