GCSE Plus student Shanique Wilson runs every day, so she decided to use her OCN maths project to investigate how running affects her, and how the choices she makes affect her running. For several weeks, she kept records of distances, routes, times of day, days of the week, locations, biological indicators and other measures.
She investigated several interesting links between variables, including the differential between base heart rate and the raised rate after a run. Particularly surprising, though, was the discovery of a strong association between the length of time a run lasts and the end pulse rate, regardless of the start rate. The relationship was not a straight line, but a definite and easily sketched curve.
Having discovered this association, Shanique entered the data into a spreadsheet. Exploring different lines of best fit produced one which gave a very close prediction for end of run pulse rate from the run time in seconds.
The equation of the curve is shows that heart rate increases roughly in proportion to the fourth root of run time. The overall correlation coefficient of the prediction is R=0·94, and improves still further as the run time increases. (Click the graph image for a larger view.)
