LINEAR ALGEBRA Least squares problems play a fundamental role in mathematical modelling of real life phenomena. In economics, geography, demography and sociology, an age dependency ratio is an age-population ratio of those typically not in the labor force (the dependent part ages 0 to 14 and 65+) to those typically in the labor force (the productive part ages 15 to 64). It is used to measure the pressure on the productive population. Consideration of the dependency ratio is essential for governments, economists, bankers, business, industry, universities and all other major economic segments which can benefit from understanding the impacts of changes in population structure. A low dependency ratio means that there are sufficient people working who can support the dependent population. A lower ratio could allow for better pensions and better health care for citizens. A higher ratio indicates more financial stress on working people and possible political instability. Below are age dependency ratios for the USA for years 2000 – 2015. Find a quadratic least squares regression polynomial ? = ?0 + ?1? + ?2 ? 2 and use the model to estimate the age-dependency ratio for the year 2020. Year Age Dependency Ratio 2000 .516 2003 .505 2006 .497 2009 .495 2012 .501 2015 .512
Least squares problems play a fundamental role in mathematical modelling of real life
phenomena.
In economics, geography, demography and sociology, an age dependency ratio is an age-population
ratio of those typically not in the labor force (the dependent part ages 0 to 14 and 65+) to those typically in the
labor force (the productive part ages 15 to 64). It is used to measure the pressure on the productive population.
Consideration of the dependency ratio is essential for governments, economists, bankers, business, industry,
universities and all other major economic segments which can benefit from understanding the impacts of
changes in population structure. A low dependency ratio means that there are sufficient people working who
can support the dependent population. A lower ratio could allow for better pensions and better health care for
citizens. A higher ratio indicates more financial stress on working people and possible political instability.
Below are age dependency ratios for the USA for years 2000 – 2015. Find a quadratic least squares
regression polynomial ? = ?0 + ?1? + ?2 ?
2
and use the model to estimate the age-dependency ratio for the year 2020.
Year Age Dependency Ratio
2000 .516
2003 .505
2006 .497
2009 .495
2012 .501
2015 .512
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