Introduction to Regression (Dr. Monticino)

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Introductionto Regression(Dr. Monticino)
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Assignment Sheet Math 1680

• Read Chapter 9 and 10
• Assignment 7 (Due March 2)
• Chapter 9
• Exercise Set A 2, 6, 7, 8 Exercise Set B 3,
  4
• Exercise Set C 1, 2 Exercise Set E 3, 4, 5
• Chapter 10
• Exercise Set A 1, 2, 4, 5 Exercise Set B 3
• Exercise Set C 1 Exercise Set D 1, 2
• Exercise Set E 1, 2
• Test on March 2 on Chapters 1-5, 8, 9, 10.
• Emphasis on problems, concepts covered in class
  and on quizzes

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Regression

• Regression is used to express how the independent
  variable(s) is (are) related to the dependent
  variable
• And, to make predictions about the value of the
  dependent variable based on knowledge of the
  value of the independent variable
• In particular, regression is used to build a
  linear model to describe the relationship between
  the independent and dependent variable

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Regression
FE score a b(MT score)
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Regression Line

• The regression line is to a scatter diagram as
  the average is to a list.
• The regression line for y on x estimates the
  average value of y corresponding to each value of
  x

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Linear Regression Model

• Again, the regression line provides a linear
  model for predicting the value of the dependent
  variable given the value of the independent
  variable
• If there was no correlation between the variables
  then a reasonable guess for the value of the
  dependent variable would be the Ave(Y)
• If there was very strong correlation between the
  variables, say correlation 1, then given a value
  X Ave(X) kSD(X), then one
  should guess Y Ave(Y)
  kSD(Y)see next slide for details

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Linear Regression Model

• Equation of the Regression Line
• (Notice its relationship to the
  SD Line)

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Origins of Regression Line

• Regression line is the smoothed version of the
  graph of averages

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Graph of Averages
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SD and Regression Lines

• r .99 Yellow Regression
  Line Purple SD Line

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SD and Regression Lines

• r .89 Yellow Regression Line Purple SD
  Line

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SD and Regression Lines

• r .75 Yellow Regression
  Line Purple SD Line

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SD and Regression Lines

• r .54 Yellow Regression Line
  Purple SD Line

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SD and Regression Lines

• r .12 Yellow
  Regression Line Purple SD Line

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Regression Example

•  A Denton consumer welfare group investigated the
  relationship between the size of houses and the
  rents paid by tenants. The group collected the
  following information on the sizes (square feet)
  of six houses and monthly rents (in dollars) paid
  by tenant

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Regression Example

• Draw a scatter plot
• Find the correlation coefficient between the size
  of house and the rent paid
• Give the equation for the SD line
• Graph the SD line
• Find the equation for the regression line
• Graph the regression line

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Regression Example

• Use the regression line model to predict the rent
  for a 1400 sq. ft. house
• Suppose that you do not know the square footage
  of the home, how much would you expect to pay for
  rent?

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Scatter Plot
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Regression Example
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SD Line

• SD line passes through the point
  (x-average,y-average) and has slope (/- ) (SD of
  y)/(SD of x)

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SD Line
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Regression Line
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Regression Line
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Prediction

• Rent for a 1400 sq. ft. house
• Suppose that do not know the square footage of
  the home, how much would you expect to pay for
  rent?

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Regression Tidbits

• Regression effect
• Regression fallacy
• Two Regression lines

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Two Regression Lines

• Often there are not clear cause and effect
  variables
• In such cases, it may be just as reasonable to
  regress either variable with respect to the other
  
• However, need to be clear which variable is being
  considered the dependent variable (the value
  being predicted) and which variable is being
  considered the independent variable in the
  regression application

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Two Regression Lines

• Example
• Suppose the correlation between husbands and
  wifes IQs is .6. The average husband IQ is 100
  with an SD of 10, the average wife IQ is 105 with
  an SD of 8
• Given a husband with an IQ of 110, use regression
  to estimate his wifes IQ
• Given a wife with an IQ of 100, use regression to
  estimate her husbands IQ
• 
  
  
  (Dr. Monticino)
• Chapter 9 Review exercises 2, 3, 5, 8
• Chapter 10 Review Exercises 1, 2, 3, 5, 7