1. LINEAR REGRESSION: On to Predictions! Or: “How to amaze your friends and baffle your enemies”

2. Imagine: The correlation between 1 mile run time and VO 2 Max is r = -1.0!

3. Suppose you know... that a 6:30 mile = 40 ml/kg/min and 6:00 mile = 45 ml/kg/min Could you predict what VO 2 Max a person would have who could run a 5:00 min mile???

4. Of Course you could, by finding the equivalent point on the line!

5. Mile Time vs. VO 2 Max MILE TIME VO2 MAX 4:004:305:005:306:006:30 40 45 50 55 60 r = -1.0

6. 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

7. More Math?? Y=a+bX General formula for a straight line Calculated from the means, s, r

8. 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)

9. Linear Regression Maybe you recognize this general equation: Y = a+bX: VO 2 = 111.33 - (0.42 * HR) Y = a + (-b * X) Y = dependent variable X = independent variable

10. 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

11. Mile Time vs. VO 2 Max MILE TIME VO2 MAX 4:004:305:005:306:006:30 40 45 50 55 60 r = -1.0

12. Get Real! In the REAL WORLD, it is never so tidy There is some deviation between the line and most points

13. 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

14. Note the error from predicted? R =.87 Prediction Line Actual Scores

15. Body Composition data: Compared to UWW Skinfold 7 site Skinfold 3 site BIA Infrared Circumference 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%

16. Let’s 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!