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Function Modelling Using Secondary Data from E-STAT

In the real world, graphs related to human population or socio-economic statistics rarely approximate any mathematical functions other than linear functions.  However, there are some occasions where the underlying conditions lead to trends which closely approximate quadratic, exponential, sinusoidal, and logistic functions.

Provided below are examples where real world data from Statistics Canada surveys can be approximated by function models.  All data are extracted from E-STAT, a database available to registered educational institutions, depository libraries, teachers, and students at no charge.

Linear

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Topic	Years	Table Number	Vector Number
Total population	1971 to 2005	051-0001	v466668
Median age	1971 to 2005	051-0001	v466689
Movie theatre ticket prices	1996 to 2001	501-0010	v26563414
Revenue of fitness centres	2000 to 2004	361-0002	v1885072
Energy use by the business sector	1993 to 2000	153-0032	v29505744
Total pregnancies	1992 to 2000	106-9002	v14225258
Enterprises with a website	2000 to 2005	358-0008	v2651352
Life expectancy	1979 to 1999	102-0025	v5939197
Bottled water	1995 to 2001	002-0011	v783736
Military personnel **Piecewise Linear**	1969 to 1998	183-0004	v130106

Quadratic

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Topic	Years	Table Number	Vector Number
Canadian Births **Convert to "Annual (sum)" under Manipulate data**	1948 to 1968	053-0001	v62
Number of males registered in trade programs	1991 to 2001	477-0051	v21691205
Number of homicides by shooting	1978 to 1982	253-0002	v1489239
Absence rates of full-time female employees in processing, manufacturing, and utilities	1987 to 1992	279-0031	v1406646

• Lesson Plan: Quadratic Modelling of the Number of Males Registered in Apprenticeship Programs (view)

Exponential

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Topic	Years	Table Number	Vector Number
Federal debt	1955 to 1997	385-0010	v151537
Consumer price index	1951 to 2005	326-0002	v737344
Farm value of potatoes	1908 to 2004	001-0014	v47184
Absence rates of full-time female employees in occupations in social science, education, government service, and religion	1997 to 2002	279-0031	v1406511

Sinusoidal

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Topic	Years	Table Number	Vector Number
Population aged 20-24	1971 to 2005	051-0001	v466758
Employment in the public sector **Convert to "Annual (average)" under Manipulate data**	1981 to 2005	183-0002	v135015
Production of beer	2000 to 2003	303-0019	v1552
Imports of fresh fruits and berries	2000 to 2004	226-0002	v212580
Induced abortions for women under 20 years of age	1974 to 2003	106-9034	v31232487
International travelers into Canada	1999 to 2006	387-0004	v81688
Employment rate	2002 to 2006	282-0001	v2091219

Logistic

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Topic	Years	Table Number	Vector Number
Cable television industry revenues	1976 to 2000	353-0001	v81330

Extracting Data from E-STAT

1. Go to the E-STAT website at http://estat.statcan.ca.
2. Click on Search CANSIM on the left sidebar.
3. Now you have two options:

• To get an exact graph, as presented, type the Vector Number into the search box.
• To select alternatives for the variables, type the Table Number into the search box and then select values for each of the dimensions.

4. On the Subset selection page, once you have selected all your variables, click on the Retrieve as individual Time Series button.
5. On the Output specification page, select the type of graph or table you wish to have displayed and then click on the Retrieve now button.

• If you wish to have students use the data in a separate data analysis program, select Plain text: Table, time as rows, and then cut and paste the data.
• If you wish to display a graph within E-STAT, Line graph, Line graph with symbols, and Scatter graph usually work well.

Suggestions for Classroom Use

1. Have students research the reasons (historical, social, economic, etc.) why certain data follow certain patterns. 
   Suggestions:

• See footnotes attached to the tables for more information.
• See The Daily attached to the tables for a summary of data trends which is linked directly under the table name as "View latest article from The Daily related to this table".

2. Have students import the data into a data analysis program and fit a function to the data by altering variable values.
3. Sample graph outputs for teachers:
   • Linear
   • Quadratic
   • Exponential
   • Sinusoidal
   • Logistic