LINEAR REGRESSION: On to Predictions!

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LINEAR REGRESSION On to Predictions!

• Or How to amaze your friends and baffle your
  enemies

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Imagine

• The correlation between 1 mile run time and VO2
  Max is r -1.0!

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Suppose you know...

• that a 630 mile 40 ml/kg/min
• and 600 mile 45 ml/kg/min
• Could you predict what VO2 Max a person would
  have who could run a 500 min mile???

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Of Course you could, by finding the equivalent
point on the line!
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Mile Time vs. VO2 Max
60
r -1.0
55
VO2 MAX
50
45
40
400
430
500
530
600
630
MILE TIME
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Describing and Defining the LINE

• To describe a line on a graph, we need to know
• The slope
• The point where the line intercepts the y axis

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More Math?? YabX

• General formula for a straight line
• Calculated from the means, s, r

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Y a b X

• Y the predicted value of y for a given value of
  X
• a the point of the y intercept
• b the slope of the line (rise over run)
• X the value of X ( Height) for predicting Y
  (Shoe size)

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Linear Regression

• Maybe you recognize this general equation Y
  abX
• VO2 111.33 - (0.42 HR)
• Y a (-b X)
• Y dependent variable
• X independent variable

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How Accurate is the Prediction?

• When the correlation coefficient is equal to 1.0,
  then every actual score will fall exactly on the
  prediction line.
• THERE IS NO ERROR BETWEEN THE ESTIMATED
  PREDICTION and REALITY

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Mile Time vs. VO2 Max
60
r -1.0
55
VO2 MAX
50
45
40
400
430
500
530
600
630
MILE TIME
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Get Real!

• In the REAL WORLD, it is never so tidy
• There is some deviation between the line and most
  points

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Standard Error of Estimate

• The predicted (estimated) score will not be
  exact, there will be a margin of error between
  predicted and actual scores.
• Thus we need to know the standard deviation of
  the prediction error.
• The SEE gives one a feel for the accuracy of a
  prediction

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Note the error from predicted?
Prediction Line
Actual Scores
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Body Composition data Compared to UWW

• Skinfold 7 site
• Skinfold 3 site
• BIA
• Infrared
• Circumference

• r.87 SEE 3.5
• r .87 SEE 3.5
• r.80 SEE 5.0
• r .80 SEE 4.5
• r .75 SEE 7.0

UWW vs dissection SEE 2.0
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Lets give it a try!

• Lab 4 Predicting Shoe size (dependent variable
  - Y)
• From Height (independent variable - X)
• First derive the linear regression equation, then
  try it out!

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