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An Example

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... (oz) Temperature ... Water Consumption (oz) Temperature (F) Day. Back to our example. Best Fit Line ... person's water consumption will be about 46 ounces. ... – PowerPoint PPT presentation

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Title: An Example


1
An Example
Taken from http//www.mtsu.edu/rowell/regression/
index.htm
2
Scatterplot
3
Correlation
  • Correlation between temperature and water
    consumption is r0.963. What does that mean?
  • http//stat-www.berkeley.edu/stark/Java/Html/Corr
    elation.htmhttp//www.stat.uiuc.edu/courses/stat
    100/java/GCApplet/GCAppletFrame.html

4
Correlation is not Causation
5
Back to our example
6
Best Fit Line
7
Which line is best?
  • http//www.ruf.rice.edu/lane/stat_sim/reg_by_eye/
    index.html
  • We are minimizing the mean square error.

8
Formulas
  • Theoretical model
  • Model based on data

Unknown parameters
Random error
Estimated values based on data
9
Formulas
Slope of regression line
Intercept of regression line
10
Back to our Example
  • Consumption 1.5 Temperature 96.9

Slope
Intercept
Slope If temperature increased by 1 degree, how
much would consumption increase?
Intercept If the temperature was zero, how much
would consumption be?
11
Back to our Example
  • What is the expected water consumption when the
    temperature is 95 degrees?
  • Consumption 1.5 Temp 96.9
  • 1.5 95 96.9 45.6
  • We predict that when the temperature is 95
    degrees, this persons water consumption will be
    about 46 ounces.

12
Extrapolation and Interpolation
  • What would the water consumption be if the
    temperature was 60 degrees? 40 degrees? 120
    degrees?
  • Be careful predicting beyond your data.

13
Other types of models
Linear
Quadratic
Exponential
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