This page describes the data, my methods of analysis and results for the above task.

I used MS Excel 2003 to make all the visualizations.

Data
 The following sets of numerical data were available:-
Item Unit Start End Aggregation (averaged)
Electricity kWh/day Aug-1998 Mar-2009 Monthly
Natural gas therms/day Aug-1998 Mar-2009 Monthly
Water gallons/day Aug-1998 Jan-2009 Bi-monthly or tri-monthly
Temperature degree F Aug-1998 Mar-2009 Monthly
 
Here is the first plot of the data I made  a simple line chart with one series each for the 3 utilities, and one series for the temperatures. It gives a clear idea about the scale relationships between the items.
Data-as it is

To enable visual comparision between the series, I scaled up gas by a factor of 10, and scaled down water by a factor of 3. At this point, there is no assumption about existence or absence of relationships between the items. The image may not make much sense unless you try to look at 2 items at a time (a while later).

data scaled
 

Supplementary data
Temperature: The temperature records for Chicago were initially obtained from the bills of the gas / electric company. To verify correctness of the data I compared the values against temperature records off the goverment website National Weather Service Weather Forecast Office ( backed by NOAA data I suppose)

 The data here is aggregated by month. Each column in a given set (month) of columns, indicates the difference between the temperature value reported on the bill in that month, and the temperature value recorded by NOAA.
You may want to see the aggregation by year.
The difference shown here is in absolute terms (degree F). A percentage (%) difference chart can be seen here. But it is not an accurate picture of differences, since the maximum temperature above 0 varies by season.
temperature difference from NOAA data
Electricity utilised by various appliances: The advise was to look up this data from a few websites and cross-reference to establish the reliability.
I used the following web pages for this purpose.
Water usage: I used the data provided in the exam description, after cross-referencing with http://www.kingcounty.gov/environment/wastewater/WaterConservation/Tips.aspx>
 


Analysis
 

Seasonal Trends - Macro Patterns
There seems to be a strong co-relation between temperature and the energy utility usage, but water usage is pretty independent. So, I observed water usage separately from the other two items. 

First, energy.
It is very clear that temperature affects the energy usage throughout the year. During winter natural gas used for heating and in summer electricity used for cooling, both show trends as per the temperature.

Seasonal Trend for energy


Looking at the series, we can come up with a crude estimate that in this household, following is the usage pattern.
 
The May conclusion is based on the fact that E bill starts increasing in May, but at the same time, the G bill has not yet reached its lowest levels. I deduce this happens because at this time, the temperature is just cold enough to have the heater work during the evening and/or night, while during the day the air conditioner is at work.
Also, this explanation might be off the mark. It simply can be the case that the space heater is being used more often in these months, and the central heat anyway turns on less often due to higher temperatures of approaching summer.

 Similar argument applies for the Oct month. The following bubble charts make the case stronger for natural gas heating being used in October, but not as much in May.
Electric Bubble Gas Bubble
   

After observing above charts, I came up with a revised cycle of the heating and cooling...

An additional guess - the thermostat is set to around 65-68 F. This can be deduced by studying the line series; the gas usage starts peaking every year once the temperature crosses around 65.
Next, water
The only seasonal pattern pretty evident is the abrupt increase of water usage in beginning May-June, uptil September-October. The peaks occured during Aug-Sep.

During the remaining time of the year water usage more or less is the same. One important thing here is that the water bill was trimonthly till 2001, and bimonthly thereafter through most of the data. This makes it difficult to fit a pattern.
Hence, when observing the bubble chart, one must keep in mind this fact.		 The high water usage levels during summer (June-Sep) could be explained by additional people in the household. However the consistency of the pattern across years leads me to believe that this is caused by a regular activity during summer (gardening fits here). There is also an unexpected increase startign Oct 2006, lasting through Nov 2007. This fits the description of vigorous gardening.
 

Statistical
A statistical analysis can bring forward outliers. I performed a simple analysis, in which I visualize the variance of each value from the mean. The mean is calculated by grouping the years together for every month. The standard deviations and mean are plotted in graphs below the variance visualization. I found this analysis feasible because the years drawn as series over the month axes, are pretty cohesive for both the electricity and gas (gas is extremely cohesive). So it is clear that they bundle up around a mean value each month.

ELECTRICITY - variations from monthly means  (grouped by Month)
 The mean and std. deviation chart indicates that the electricity usage is about 21 kWh during the winter (when the AC is not functional). Assuming the statistics given about the usage of various appliances, that leaves a gap of about 4 - 5 kWh unaccounted. This would account for the lighting + refrigeration cost, which were not mentioned in the task desciption. lighting cost per day.
Refrigeration might use between 0.8 - 1.5 kWh, assuming a relatively new appliance (add another 1 kwH if a separate freezer is used). This leaves about 1.5-2.5 kWh going for lighting. Given this estimate, it might be possible to estimate the number of ligthing  appliances (??) and thus the size of the house (??).
ELECTRICITY - variations from monthly means  (grouped by Year)
The following observations were made:-
Concentrating on summer months, there seems to be a drop in electricity usage starting 2005. In 2005, the stats are pretty much near the mean (while they should be high) or downward. This trend continues more or less in the years later. Since AC is the biggest player in summer months, we can deduce the following.

Deduction: During 2005 or 2006 summer, the more efficient AC was in action.  It is possible also that it was around 2006 that the hosuehold started using a  programmable thermostat.
 
GAS - variations from monthly means  (grouped by Month)td>
The average use for activity other than heating seems to be about 0.8 therms.
GAS - grouped by Year

There is a distinct drop in usage starting Jan 2006. This could be attributed to higher temperature during that season. However, the pattern continues into the next year too, where the temperatures were pretty low relative to the entire set.
This strengthens the deduction that the programmable thermostat came into play somewhere during 2006.
 
 

WATER
For water, I presumed a normal usage level of 90 gallons/day for day to day activities (after observation) and used this to see offsets which might be interesting.
WATER - variance from 90 gallons/day
 
 
WATER - grouped by Year
Deductions:
1) Somewhere in 2003 end, the washing machine was replaced.

2) During June-Sep from 2002-2006, there seems to be 1-2 more persons in the household than during other months.

3) Adding to the water usage during the months in point 2 also could be gardening during summer months.

4) If intense gardening was started mid 2006 (summer), then mulch came into the picture somewhere during the end of 2007.
 However,high amount of watering during winter might not be the case, and so that indicates that there were guests in the house somewhere in the end of 2006 too. ???