Embedded Files
Assumptions
Assumptions
The City of Scottsdale is a perfect rectangle. We know that realistically, the city does not fit the format of a perfect rectangle. However, as our equations will be primarily considering the total area of the city and the number of objects in a grid, this assumption should not have a significant effect on the calculations as the city is organized into a mostly grid-like pattern.
There is an average # of houses per grid (0.5 miles by 0.5 miles)
Scottsdale is defined by the borders shown on the map that was provided by the City of Scottsdale website.
There is an average size for housing units (We are assuming this number to be approximately 1,600 sq feet)
Apartments, Condos, and Townhouses are considered housing units but are not considered houses. We will attempt to account for these in our model. However, there is no discernable pattern or method of measuring how many individual housing arrangements are contained within a single building or complex. There are also no standards for how big a complex can be or how tall the buildings can be. Since we cannot accurately measure the number of "house equivalent" arrangements within these areas, we will be excluding these values from the final estimation for the number of houses in Scottsdale.
Constraints
Constraints
Time (10 days to work on this.)
Entirely conceptual, no prototypes
Limitation on skills
Limitation on information
Limited to digital measurements.
Tools
Tools
Visualization and Logic:
One of the tools we used is logic and visualization, where when we observed the map of Scottsdale, we found that it was split up in to areas that are made of grids, which we used to help make estimating easier.
Measuring:
We also used measuring as one of the tools we used, as we had to measure the grids that we found from the visualizing and logic tool above. We found out that each of these grids is .5 miles x .5 miles, and this gave us a great idea of how large these grids are and how many houses could fit in these grids.
Counting:
One of our most used tools was the simple method of counting. With this tool, we were able to find the average number of houses in a standard half-mile by half-mile grid by taking screenshots of the city map in satellite view and then manually counting the number of houses in a sample grid.
Math:
Another really useful tool we used was math. Using simple addition and multiplying, we were able to create a bunch of formulas and steps, which we used to find our total number of households in Scottsdale.
Assessment
Assessment
Usefulness:
The usefulness of a model is defined by the accuracy of the data being produced by it. Depending on the required accuracy of the model's application, our model can be moderately useful. if the application is the collection of census data, then our model may not be the preferred tool. However, if the intent of the model's application is to get a rough semi-accurate estimation of the total real estate, then our model can be quite useful.
Assessment:
Using the data we collected, we estimated the total number of households in Scottsdale to be 108,195. The number of households in Scottsdale provided by the official US Census Bureau is 115,401 houses. According to this number of houses, our model is accurate to within 6.2% or roughly 7,000 houses, which is moderately close to the official calculation and makes our model potentially useful. The sources of error in our calculations are likely due to a number of assumptions we made throughout the project that could have been more accurate.
To make our final calculations, we will use the equation progression that was laid out in Section 1: Algorithm and replace the variables with the values that we collected in section 2: Data.
The first variable that will be substituted with our collected data will be the total area of Scottsdale. This value was measured to be 184.7 sq mi.
The equation becomes:
184.7 sq mi = Area of houses + area of everything else
Rather than determine the average area of a house, we decided to simplify this calculation by replacing the total area with a number of grids. To find this value, we did the following:
Total number of grids = Total Area / Grid area
Therefore,
184.7 / 0.25 = 738.8 grids
The next step was to determine the types of neighborhoods in Scottsdale. These were determined to be Rural, Suburban. Urban, and Mixed-use. We found the concentrations of these areas to be 33%, 25%, 5%, 12% respectively. After this step, we need to determine the number of grids for each type of grid. The process for determining these values is as follows:
Number of grids (type) = Total number of grids * %grid type
Number of Rural grids = 738.8 * 33% = 243.804 grids
Number of Suburban grids = 738.8 * 25% = 187.4 grids
Number of Urban grids = 738.8 * 5% = 36.94 grids
Number of Mixed-use grids = 738.8 * 12% = 88.656 grids
Now that we have a total number of grids for each type of neighborhood, all we need to do is multiply the number of each type of grid by the number of housing units in that type of grid. This calculation will give us the total number of housing units for each type of neighborhood. This calculation is shown below. See Section 2: Data to view the average housing unit calculations.
Number of housing units (type) = Number of grids (type) * Number of housing units per grid (type)
Number of Rural houses = 243.804 grids * 40 houses = 9752.16 or 9,752 houses
Number of Suburban houses = 187.4 grids * 354 houses = 66339.6 or 66,340 houses
Number of Urban housing units = 36.94 grids * 1673 housing units = 61,800.62 or 61,801 housing units
Number of Mixed-use housing units = 88.656 grids * 370 housing units = 32802.72 or 32,803 housing units
The final step in the process of calculating the total number of housing units is to add up the number of houses for each type of neighborhood. Due to the inconsistencies involved with calculating the number of housing units in the urban grids, we will be calculating the total number of housing units twice. The first calculation will include the Urban housing units, while the second calculation will not. This calculation is below.
Total number of houses = number of rural houses + number of suburban houses + number of urban houses + number of Mixed-use houses
9,752 + 66,340 + 61,801 + 32,803 = 170,696 housing units (Including Urban areas)
9,752 + 66,340 + 32,803 = 108,895 housing units (Not including Urban areas)
Therefore, The total number of housing in Scottsdale is 170,696 if we include apartments, condos, and townhouses. 108,895 of these housing units are distinctly houses.
Excel Spreadsheet
Fig. 30: Excel calculation spreadsheet
Access to this spreadsheet and its calculated columns can be found here
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