I have observed that I am generally in a better mood after exercising. If I record data on how much I exercise and my mood, how can I correlate these?
Input: discrete events recorded at irregular, unpredictable intervals. Example input data:
- Monday 2pm - Exercise (Moderate, 4/10, or 0.4)
- Monday 5pm - Mood (0.5)
- Monday 9pm - Mood (0.4)
- Tuesday 10am - Mood (0.6)
- Tuesday 12pm - Exercise (Intense, 0.9)
- Tuesday 1pm - Mood (0.7)
- Tuesday 7pm - Mood (0.7)
- Wednesday 1pm - Mood (0.6)
- Thursday 10pm - Mood (0.6)
- Assume observations like these continue for months
- Correlation strength (how strongly correlated are these?)
- Correlation error (margin of error - what are the odds this correlation is an anomaly of too little data?)
- Correlation phase (are they correlated on a delay - ie does mood rise 30 hours after exercise?)
Note that you cannot assume any kind of line/curve between data points - they are discrete events (in my example - 0.5 exercise on Monday and 0.8 exercise on Tuesday does not mean a steady increase in exercise overnight). Also note that "mood" and "exercise" are arbitrary - they could be swapped out for "vegetables eaten" and "wifi speed".
Looking for the theory at this point, I am not ready to actually do the calculations.