Simple Linear Regression

1
Simple Linear Regression

• Often we want to understand the relationships
  among variables, e.g.,
• SAT scores and college GPA
• car weight and gas mileage
• amount of a certain pollutant in wastewater and
  bacteria growth in local streams
• number of takeoffs and landings and degree of
  metal fatigue in aircraft structures
• Simplest relationship ?
• Y a ßx

2
Example

• The owner of a small harness race track in
  Florida is interested in understanding the
  relationship between attendance at the track and
  the total amount bet each night. The data for a
  two-week period (10 racing nights) is as follows

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Estimating the Regression Coefficients

• Method of Least Squares
• Determine a and b (estimates for a and ß) so
  that the sum of the squares of the residuals is
  minimized.
• Steps
• Calculate b using
• and a using

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For Our Example

• b _______________________________________
• a ______________________________

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What does this mean?

• We can draw the regression line that describes
  the relationship between attendance and amount
  bet
• We can also predict amount bet based on
  attendance.

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How good is our prediction?

• Estimating the variance
• Coefficient of determination, R2
• a measure of the quality of fit, or the
  proportion of the variability explained by the
  fitted model.

(see next page)
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Calculations
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Or Using Excel