Running Resolution

Research Question: What effect does the frequency of running have on the time it takes to run a mile?

Explanatory Variable: Frequency of running.

Response Variable: Time it takes to run a mile.

- Run a mile everyday for thirty days.
- Run the same course each time.
- Measure the time it takes to run a mile, with a stopwatch, in minutes and seconds. Time will begin at start of run (mile 0) and end at end of run (mile 1). Miles will be measured using a GPS
device and marked on the grass with spray paint. Frequency of running will be measured in days.

Expected Association: I expect there to be a negative correlation because I expect that the time it takes to run a mile will decrease as the days of running increases (the more in shape one gets, the faster they run).

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Correlation Coefficient, r = -0.969
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Coefficient of Determination, R^2 = r^2 = 93.8%

Least Square Regression Equation:
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Discussion: The correlation coefficient, r, proves the expected association of there being a negative correlation between variable. With a r-value of -0.969 there is a strong negative linear relationship between the explanatory variable and the response variable. It can be seen that if the frequency of running increases by one day, the mile time decreases by 0.0027 minutes, or 0.162 seconds. An interpretation of the y-intercept cannot be given because it is outside the scope of the model. 93.8% of the variation in mile time is explained by the least-squares regression line, and 6.2% of the variation in mile time is explained by other factors. Some lurking variables that could have affected mile time include:
  • weather; especially windy conditions during Superstorm Sandy made it incredibly harder to run than during 'normal' conditions.
  • health conditions; an occurrence of strep throat decreased ability to push harder during runs.
  • other exercise performed during this time.
  • lifestyle activities; including amount of alcohol drank the night before a run and diet.
  • preconceived notion; I think that creating an expected association before collecting data had me wanting to try hard to 'prove' this association.