Math 30-2 Project

Calgary Population

I chose this particular project because I find it is interesting to see our city’s increasing overall
population. My goal is to demonstrate the increase of population in Calgary.

Year (L1)	Population (L2)	Difference (compared to previous year)
1990 (0)	692,885
1991 (1)	708,593	15,708
1992 (2)	717,133	8,540
1993 (3)	727,719	10,586
1994	738,184	10,465
1995	749,073	10,889
1996	767,059	17,986
1997	790,498	23,439
1998	819,334	28,836
1999	842,388	23,054
2000	860,749	18,361
2001	876,519	15,770
2002	904,987	28,468
2003	922,315	17,328
2004	933,495	11,180
2005	956,078	22,583
2006	991,759	35,681
2007	1,019,942	28,183
2008	1,042,892	22,950
2009	1,065,455	22,563
2010	1,071,515	6,060
2011	1,090,936	19,421
2012	1,120,225	29,289
2013	1,156,686	36,461
2014	1,195,194	38,508
2015 – estimation	1,211,602	16,408
2016 – estimation	1,239,847	28,155
2017 - estimation	1,268,751	28904

Data acquired from here (http://www.calgary.ca/_layouts/cocis/DirectDownload.aspx?target=http%3a%2f%2fwww.calgary.ca%2fCA%2fcity-clerks%2fDocuments%2fElection-and-information-services%2fCensus2014%2fFinal%202014%20Census%20Results%20book.pdf&noredirect=1&sf=1) at page 20.

I began with year 1990 and ended with year 2014. Since we are still in year 2015, the population of Calgary on that year will be estimated. The population of Calgary reached one million in year 2007. There were some annexations in year 1996, 2005, and 2008. The annexation slowed down the population growth slightly.

Exponential Regression Graph

After I gathered the data from the link above, I created an exponential regression graph. The exponential regression is as follows:

Y = 681007.50380284(1.0233125727547)^x

This graph is the most accurate compared to other graphs below. The plot points are mostly touching the line. The most beautiful graph as well…

Calgary’s population continues to expand. By using table of values and the regression provided above, in year 2017, Calgary are predicted to have about 1,268,751 residents. In year 2025, 1,525,608 citizens are estimated to live in the city.

Linear Regression Graph

Y = 659736.50153846+20894.001538462x

Linear graph is not ideal because the scatter dots are way off from linear regression.

Quadratic Regression Graph

Y = 266.00613154961x^2+14509.854381271x+684209.06564102

Much better than linear regression graph. However, I still think that scatter dots still are off a bit compared to exponential graph.

Cubic Graph

Y = -10.553894012575x^3+645.94631600231x^2+10936.305868613x+690617.39008546

This graph is not too bad, either. However, I don't think that Calgary's population are decreasing anytime soon, unless some factors caused the population to decrease. It is good idea to use this graph if the population is estimated to decrease after a certain number of years.

Conclusion

The exponential regression graph is the most accurate graph, followed closely by quadratic regression graph. Cubic regression graph is best suited to project the population decrease. Linear regression graph, however, is the most inaccurate graph above all.

Reference(s)/source(s)