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I'm having a hard time explaining this (hence the weird and long title), also I'm not a mathematician, I have this data lying around in a database and was wondering how I could visualise it (and predict the future)

Say I gave you the following data for one user, it can show anything, for example say it shows whether someone ran on a certain day (or completed any other task):

Date            Done?
19/05/2011      yes 
18/05/2011      no
17/05/2011      no
16/05/2011      no
15/05/2011      no
14/05/2011      yes
13/05/2011      yes
12/05/2011      yes
11/05/2011      yes
10/05/2011      no
9/05/2011       yes
8/05/2011       no
7/05/2011       no
6/05/2011       yes
5/05/2011       no
4/05/2011       yes

I have a couple of questions:

  1. What data could you derive from this? How can this be represented (other than pie charts, bar charts and totals).

  2. Is there anyway to predict what they would do tomorrow?

  3. I used Lower bound of Wilson score confidence interval for a Bernoulli parameter to figure out a score... what does this mean, is this useful in anyway?

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migrated from math.stackexchange.com May 19 '11 at 16:16

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I don't think my comment is worthy of a separate answer, but since you are doing daily samples, one thing to look for is patterns based on conventions that won't be inherently obvious from the data set. Consider if there is a weekly or monthly pattern, for example, which may be stronger than other intervals. For something like running, you would also need to consider a weather overlay to see if rain affected the outcomes if it occurs outdoors. –  nycdan May 19 '11 at 16:24
    
The term time series analysis should be somewhere on this page. –  ziggystar Mar 2 '12 at 14:03

2 Answers 2

You can have a look at this "Mind Reading" game and at the details of its implementation. I think it is very relevant to your second question.

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Simply construct a Transfer Function Model and include 6 dummies representing days of the week , then bring in 51 dummies representing weeks of the year , then incorporate 15-7 national holiday/event indicators. Then estimate an OLS model and identify any unusual data such a a missed monday even though he had been very reliable on monday given that it was not an event. Validate that the runner has not decided to take certain days of the week off starting at some point in history. This plus a ton of other things ( like identifying that he never runs on certain days of the month ) get incorporated into predictions that we make for millions of series every day.

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