two variables and determines the probability of the relationship occurring by chance. Also,
validity of the results is increased as there are no assumptions made.
Map 1: Area of Investigation
Hypothesis
For the East, West, and North transects, it was predicted that as distance from the YDI increases, the price of parking from 7:00 AM to 6:00 PM in any parking lot will decrease by 50% per kilometer. Therefore, the price of a parking lot 1.3 kilometers from the YDI will be half the price of a parking lot .3 kilometers from the YDI. The reasons are that because the YDI has the most expensive land values in the city, the parking rates will be highest there. As a result, it can be deduced that as the land value decreases, the price of parking will as well. The rate of 50% decline in price per kilometer was chosen because it did not seem overly ambitious in terms of change in price.
For the South transect, it was predicted that as the distance from the YDI increases, the price of parking from 7:00 AM to 6:00 PM in any parking lot will increase by 50% for privately owned parking lots but decrease at the rate of 25% per kilometer for municipal parking lots. The reasons are that as one moves southwards from the YDI, the Toronto Harbourfront is approached. The Harbourfront offers many attractive features to potential residents: newly built condominiums, waterfront properties, proximity to downtown Toronto, and the Toronto Harbourfront Center, a “cultural center that has song and dance, art and theater, everything you need for a mesmerizing cultural experience” (Benson). The Harbourfront Center has performing and visual arts showcases, children’s programs, and other offerings that increase the desirability of living in the Harbourfront area and increase parking prices because of higher demand for housing and, subsequently, parking.
Data Collection
Table 1: Parking Lots East of the YDI
Picture 2: Parking Lot E2
Table 2: Parking Lots West of the YDI
Picture 3: Parking Lot W8
Table 3: Parking Lots North of the YDI
Picture 4: Parking Lot N2
Table 4: Parking Lots South of the YDI
Picture 5: Parking Lot S8
Analysis of Data
As one can tell from the data and graphs on the previous pages, the general trend for the change in prices as distance from the YDI increases is that prices decrease, resulting in an inverse relationship between distance from YDI and price.
However, there is a drastic difference between the trend of change between the North, East, and West transects versus the South transect. The price changes in South direction increased along with distance from the YDI, indicating a positive relationship.
For the East transect, the price dropped from $15.00 to $6.00, a difference of $9.00, in a distance of 1.5 kilometers. This represents a decrease of $6.00 per kilometer, or 40% of the original price. Compared to the hypothesis, which predicted a drop of 50% per kilometer, the decrease was not as large as expected.
For the West transect, the price decreased from $18.00 to $6.00, a drop of $12.00, in a distance of 1.2 kilometers. This represents a drop of $10.00 per kilometer, or 56% of the original price, and more than the predicted change.
For the North transect, the price decreased from $12.00 to $10.00, a decline of only $2.00, in a distance of 1.1 kilometers. This is equivalent to a drop of only $1.80 per kilometer, or 10% of the original price, much less than predicted.
For the South transect, two changes will be evaluated, as the general trend was that price increased, but the last parking lot had a price that decreased from the parking lot before it. With the last lot, the price decreased by $4 (27%) from $15 to $11, a change less than expected. Without the last lot, the price increased $9 (60%) to $24, a change that was more than expected. Clearly, the last parking lot causes a substantial change in the differences in price.
Geographic Model: Bid-Rent Theory
The Bid-Rent theory is a geographic model that uses the concept of locational rent to derive conclusions as to who is willing to pay the most for a plot of land (Waugh). The theory is based on the valid assumption that the highest bidder for a plot of land will be willing to pay the most rent (Waugh). In the real-world economy, businesses tend to have more money to spend on their land rental than industrial or residential users. Therefore, as businesses have the most money, they will also tend to spend the most money on their land rentals. Industry is willing to pay less than businesses, but more than residential users (Wakefield). This is illustrated in the diagram below.
Figure 1: Bid-Rent Theory (Waugh)
The slopes and x-axis intercepts of the various lines are different because the x-axis shows the distance from the CBD. Because businesses intend to locate themselves in the CBD itself, they are not willing to buy land that is too distant from the CBD or the YDI (Wakefield). Similarly, within the CBD, residential users are willing to pay the least (Waugh). Costs are highest in the CBD because it is such a small area in comparison to the rest of the city, and demand is therefore high (Waugh). Because the highest bidder must pay highest rent, and most of the CBD is used for business ventures, the higher the costs of the land, the higher the prices will be (Wakefield). Therefore, based on the pattern observed from the data (increasing distance, decreasing price), it can be concluded that the parking prices are dependent on the land values.
In the case of Toronto, even though many people may work in the CBD, they are
willing to reside in the suburban areas because of lower prices for housing and ready
availability of public transportation on the Toronto Transit Commission’s services.
Residents of areas even farther from the CBD, such as Markham and Richmond Hill, can
use the Greater Ontario bus service to commute to and from the CBD. The map below
shows how distant these suburbs are from the CBD.
Map 2: Suburbs (Microsoft)
Statistical Test: Spearman’s Rank Correlation Coefficient
Geographic Model: Central Business Height Index
The Central Business Height Index calculates how much a single plot of land is used for CBD functions (actions carried out within the building that contribute to the business activities of the CBD) The formula is as follows:
For example, the Bank of Montreal building, which is completely devoted to CBD functions, has 72 floors (City of Toronto). Because of this, the ratio of the floor area of CBD functions to the ground floor area will be 72 to 1, giving it a CBHI value of 72. For a building to be considered as located in the CBD, the CBHI value must be at least 1 (Waugh). Using the CBHI value, it can be concluded that the Bank of Montreal is in the CBD. For the buildings in the core of the CBD, virtually all of their functions are CBD-related, so the CBHI value will essentially be the number of floors in the building.
On the other hand, there are buildings in the suburbs, including residential
structures, whose CBHI values are extremely low. An example is my house, which has
three floors and has absolutely no CBD functions. As a result, the CBHI value is 0, and it
can be concluded that the house is not in the CBD.
Statistical Test: Spearman’s Rank Correlation
The Spearman’s Rank Correlation is used to describe the degree of association (strength of relationship) between two variables: the independent variable, distance from YDI, and the dependent variable, price (Waugh).
First, both variables are listed and ranked, from greatest to smallest magnitude (Waugh). If a number of lots have the same magnitude, they are given an equal (average) ranking (Waugh). The ranks are shown in the table on the following page. Overall, 29 parking lots were studied. Then, the rank of the second variable is subtracted from the rank of the first variable, giving us a number d (Waugh). However, the number may pose a problem, as the difference could be negative. Therefore, the difference between the two ranks is squared to eliminate all negative values (giving us d2), and the squared differences of every lot are added up, to give us the sum of all the d2 values, or (Waugh). This figure is put into the equation , where n is the number of objects in the sample (29 in this case). The value of is known as r, which provides the strength of the relationship between the two variables (Waugh). The closer r is to 1 (the maximum value possible, as it indicates a perfect positive correlation), the stronger the relationship between the two variables is (Waugh). When r gets closer to -1, it indicates a good negative relationship (Waugh). That is likely to be the case for the current investigation, as increasing distance results in decreasing prices. However, a value of r that is more than .8 is considered representative of a fairly strong correlation between the two variables in question (Waugh). The table of data for the current investigation is shown below. All 29 lots are included, ranked for both distance from YDI and price of parking. Calculations for r are shown below the table.
= 5982.5
= = = -.47. Therefore r = -.47.
After completing the calculations, r is found to be -.47, indicating that the two variables of distance from YDI and parking price have a fairly weak negative correlation. However, this is probably because the South transect’s trend, which was the opposite of the trends in the other transects, caused anomalous differences and the correlation was therefore not as strong.
In addition to performing the calculations above, the possibility that the correlation occurred by chance must also be considered (Waugh). By using the graph below, the degrees of freedom(number of objects in the sample minus 2) can be plotted against the absolute value of r (-.47) and see that the chance of the correlation occurring randomly is in between 1% and 5%. Therefore, it can be said with confidence that the strength of the correlation did not occur by chance, and the correlation can be accepted with slight caution, as it is close to being a 5% probability of chance (rejection level).
Figure 2: Spearman’s Rank Correlation Significance Level (Waugh)
As a result, even with the largely opposite trend in the South transect, the correlation can be accepted. This suggests that without the complications arising from the inclusion of the South transect, the correlation would have likely been very strong, and would have probably not have had a significant probability of the correlation occurring by chance.
Evaluation of Data
As stated previously, the only anomalous transect was the South transect, whose prices generally tended to increase as distance from the YDI increased, instead of decreasing like the other transects.
Although this may seem peculiar and unexpected, it must be remembered that earlier, it was stated that as one heads southwards from the YDI, the Toronto Harbor waterfront is being approached. New condominiums and apartment buildings have been built in this area, cultural festivals are held year-round, and the attraction of living next to the harbour causes high demand for the residential properties in this area. The more people that live in the area, the more people will need parking spots, so demand for parking will increase, and price will increase as well, as shown in the diagram below.
Figure 3: Supply and Demand
In Figure 3, shown above, the graph represents the market for parking. The increase of population results in more demand for parking. The greater demand is reflected in the shift of the demand curve to the right, as shown above. The subsequent increase in the quantity demanded from Q1 to Q2 results in an increase of the equilibrium price from P1 to P2 (Parkin). This results in higher quantity demanded by consumers and higher quantity supplied by producers, although the good is at a higher price. (Parkin). The price set by the producers will increase because to run more parking lots to meet the demands of the consumers who will use the parking lots, the costs will be more for producers. Higher operational costs, such as maintenance expenses, salaries for parking lot operators, and rent will all cause increased expenses for lot owners. If the owners want to make the same marginal profit off of their investment in land and human labour, they will be forced to raise prices, and consumers will have to pay higher prices for parking.
Apart from the understandable anomaly put forth by the South transect, the general trend in the change in parking prices as distance from YDI increased was simple: the prices decreased.
There are many possible reasons for the various aberrations in the data. For example, parking lot E3 (Eaton Center) has a price identical to parking lot E2 (Dundas Square), even though it is twice as far from the YDI.
This, like the anomalous trend of the South transect, may very well be seen as an irregularity. Although it does oppose the general trend, there are reasons why the parking lot at the Eaton Centre has the same price.
The Eaton Centre is Toronto’s largest downtown shopping mall, containing almost 300 stores and services. It is visited by almost one million people every week (TEC Retail). The obvious attraction of the mall to consumers results in huge demand for parking at the Eaton Centre, which in turn causes higher prices because people are willing to pay more money for the scarce parking spots (Parkin).
The reasons for the general trend - increasing distance and decreasing price - are much more in number. The first reason, though mainly economic, is that land values are highest in the CBD Therefore, to post a profit, as most ventures in the CBD are financial setups, the owner of the land or service being offered on the land must charge a higher price than someone who runs a similar business in the suburbs. This is reflected perfectly in the parking prices. If two identical sized parking lots, owned by the same company, are considered, the one nearer to the YDI (assuming there are no other possible distortions like the Toronto Harbourfront) will invariably cost more.
Another reason is that demand for parking is much less in suburban areas than in the CBD. As mentioned in the introduction, the area of downtown Toronto is only 97 square kilometers, although it houses more than two-thirds of a million people. As a result, the demand for parking in downtown Toronto is significant, and causes higher prices, as in Figure 3.
Conclusion
It can be noted that the general trend was that increasing distance from the YDI led to decreasing prices, indicating a clear negative correlation.
The hypothesis made at the beginning of the investigation is only partially valid. As predicted, the prices in the East, North, and West transects decreased as distance from the YDI increased, and prices for parking in the South transect, except for one parking lot, increased along with distance from the YDI. The single parking lot in the South transect that followed the trend of the other three transects, rather than the trend of the South transect, was parking lot S8, a municipal parking lot whose price was $13.00 less than the parking lot before it. There are several possible reasons: that it was the only municipal lot, and lower prices result from government price controls, or that a distance of 1.5 kilometers from the YDI is too much of a distance for the prices to continue increasing. Also, the percent changes predicted were all invalid.
There are many limitations to this study. First, it would have been more desirable to survey all of Toronto’s parking lots and then draw a conclusion on the correlation between distance and price as it would provide for a more thorough investigation. Using only downtown Toronto is also not a perfect method of sampling because it is not representative of all of Toronto and the Greater Toronto Area, but rather only represents the most expensive areas in the city. Also, land values in downtown Toronto change quickly as one moves farther from the CBD and YDI. However, in the suburbs, the land values would probably not change as quickly and prices would be more balanced as a result. Lastly, it may have been better to do separate studies for private and municipal parking lots as municipal parking lots would tend to be cheaper because of government policies to control prices and prevent inflationary trends from changing prices. The lower government prices would then cause changes in the results.
However, although following the previous suggestions would make for a more complete investigation, it may not always be practical. For example, conducting a study of all of Toronto’s parking lots would definitely be more exhaustive, but the impracticality of it is apparent: it would be nearly impossible to travel around all of Toronto and obtain data for every single parking lot. Also, the focus of this study was, specifically, the changes in parking prices within a limited distance from the CBD, so within the boundaries of this investigation, it may not be entirely necessary to conduct a study for all of Toronto. This would also give rise to new complications: should the most distant suburbs be included, or should one only study the parking lots located in the city area? Should on-street parking be studied as well? Because of the tremendous difficulties that would result from conducting a completely thorough study, it is perhaps more expedient to focus on a specific area.
The many mistakes in the hypothesis suggest the need for an alternative. First, the hypothesis should not be so specific; the over focusing of a prediction is prone to error. A better hypothesis may have been: “As distance from the YDI increases, the price of parking will decrease”. This statement would have been much better supported by the data.
After completing the investigation, several questions arise: How much would the parking rates vary in a small town without a major CBD? How would parking rates change in the Toronto suburbs? If the area of investigation were extended, how might the results of the study be affected?
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