Beginner question: Available space in a warehouse I have a year's worth of data for the available slots in a warehouse. There is a data point for every minute of the year.


*

*timestamp

*available slots


The data seems to follow a certain pattern, namely, less space during the working hours, more space during the night and on the weekends.
My question is, can probability theory help me make predictions here?
How can I calculate the likelihood of the warehouse being empty, half full, full during a certain time_span / weekday combination. 
For instance, 


*

*how likely is it, that the warehouse will be mostly full between 10am and 11am on a regular Monday?

*how likely is it, that the warehouse will be empty on 2pm on a regular Thursday

 A: You can take the 60 minutes that make up the hour between 10am and 11am and add them all together, then divide by 60 to get the average. Next you can do this for every day of a month. That is, take all the averages of the hour for each day and sum them, then divide by (29/30 or 31). That will give you the average fullness of the warehouse for that hour of the day for that particular month.
Here you can see how to calculate the standard deviation, which is the square root of the variance. It is worth pointing out that Excel has these functions built in. In Excel it looks like the function is STDEV, again here is link.
That will tell you average full-ness of the warehouse. You can also calculate median, and range fairly easily as well.
The next step would be to use that data to build a model, such that the model can be used to predict the fullness of the warehouse in the future. Before I get into building a model, I would first just plot the data and take a look at what you're dealing with.
Here is a famous image, Anscombe's quartet, that argues visualizing your data, prior to just blindly calculating the linear regression of that data is important. 
In the image, the data in all four graphs have the same means and standard deviations, but clearly drastically different behaviors. Without knowing more about your data, it is difficult for me to offer more, but a simple example would be the following.
If your data said the warehouse was full during the day, and half full at night. I might model my data with a binary (0 or 1) parameter representing the daylight cycle. My model would simply say, Daylight*.5+.5. When Daylight is equal to 0, ie. it is nighttime, I have 50% full warehouse. When it's day my warehouse is 100% full. Again simple example but I hope it helps. Naturally you can make a Month parameter, perhaps a weekday/weekend parameter, etc. The complexity of your model is up to you, just remember George E.P. Box's helpful quote, "Essentially, all models are wrong, but some are useful."
Going back to our model, Daylight*0.5+0.5, how is it I know 0.5 is the correct value? Well I don't, I just made up the value. However, a smarter approach might be to take a month's worth of data and calculate the fullness at day and at night. This will likely return numbers like 0.3942 and 0.6058, which are probably more accurate values than 0.5, since they come from actual data. What you can do next is compare that model: daylight*0.3942+0.6058 to the data from the next month and check your Sum of Squared Errors. That number will tell you how far off your model is, or how much error exists. Naturally the goal is to minimize the error. No one ever has a perfect model. Also you want to be careful of overfitting. Which is essentially making your model work great on your training data for April but terrible for other months because you focused too much on making it work well for April, and not more general for every month of the year. On the flip side, maybe you want to make 12 different models, one for each month. Keep in mind if you make one model for each month you will want to train on April 2012 data and then calculate your error on April 2013 data.
Kind of lengthy but I hope this helps.
